design of reduced rank mmse multiuser detectors using random matrix methods reduced rank minimum mean squared error mmse multiuser detectors using asymptotic weights have been shown to reduce receiver complexity while maintaining good performance in long sequence code division multiple access cdma systems in this paper we consider the design of reduced rank mmse receivers in a general framework which includes fading single and multiantenna receivers as well as direct sequence cdma ds cdma and multicarrier cdma both uplink and downlink in all these cases random matrix results are used to obtain explicit expressions for the asymptotic eigenvalue moments of the interference autocorrelation matrix and for the asymptotic weights used in the reduced rank receiver

multiple solutions to a three point boundary value problem for higher order ordinary differential equations in this paper we provide sufficient conditions for the existence of at least three solutions to a three point boundary value problem for higher order ordinary differential equations the nonlinear term f in the differential equation under consideration may depend on higher order derivatives of arbitrary order and this is where the main novelty of this work lies by applying the two pairs of upper and lower solutions method of henderson and thompson as well as degree theory the existence of at least three solutions of the problem is given

hausdorff content and the hardy littlewood maximal operator on metric measure spaces abstract let x d be a complete metric measure space and be a non negative borel regular measure satisfying the doubling condition with some dimensional constant d we prove that the hausdorff content of codimension 0 denoted by h and the hardy littlewood maximal operator m satisfy the strong type inequality x m u p d h c x u p d h 0 u l loc 1 x whenever p max 0 1 d if further satisfies some reverse doubling condition with some other dimensional constant then for the endpoint case p 1 d with 0 d 0 we also obtain the corresponding weak type estimate for h and m the fundamental point in the proofs is to introduce and develop a theory of the dyadic hausdorff content h d which is a choquet capacity comparable to h and has the strong subadditivity property

harmonic measure and quantitative connectivity geometric characterization of the l p solvability of the dirichlet problem it is well known that quantitative scale invariant absolute continuity more precisely the weak a infty property of harmonic measure with respect to surface measure on the boundary of an open set omega subset mathbb r n 1 with ahlfors david regular boundary is equivalent to the solvability of the dirichlet problem in omega with data in l p partial omega for some p infty in this paper we give a geometric characterization of the weak a infty property of harmonic measure and hence of solvability of the l p dirichlet problem for some finite p this characterization is obtained under background hypotheses an interior corkscrew condition along with ahlfors david regularity of the boundary that are natural and in a certain sense optimal we provide counter examples in the absence of either of them or even one of the two upper or lower ahlfors david bounds moreover the examples show that the upper and lower ahlfors david bounds are each quantitatively sharp

carleson measure problems for parabolic bergman spaces and homogeneous sobolev spaces abstract let b p r 1 n be the space of solutions to the parabolic equation t u u 0 0 1 having finite l p r 1 n norm we characterize nonnegative radon measures on r 1 n having the property u l q r 1 n u w 1 p r 1 n 1 p q whenever u t x b p r 1 n w 1 p r 1 n meanwhile denoting by v t x the solution of the above equation with cauchy data v 0 x we characterize nonnegative radon measures on r 1 n satisfying v t 2 x l q r 1 n v 0 w p r n 0 n p 1 n q 0 moreover we obtain the decay of v t x an isocapacitary inequality and a trace inequality

classes of carleson type measures generated by capacities we introduce classes of measures in the half space mathbb r n 1 generated by riesz or bessel or besov capacities in mathbb r n and give a geometric characterization of these as carleson type measures

well posedness of quasi geostrophic equations with data in besov q spaces abstract by wavelets and multi resolution analysis we convert the bilinear estimate on tent spaces associated with besov q spaces b p p 1 2 r n to the estimates of the numerical quantities as an application we get the well posedness of the quasi geostrophic equations with initial data in b p p 1 2 r 2

semigroup characterization of besov type morrey spaces and well posedness of generalized navier stokes equations abstract the well posedness of generalized navier stokes equations with initial data in some critical homogeneous besov spaces and in some critical q spaces was known in this paper we establish a wavelet characterization of besov type morrey spaces under the action of semigroup as an application we obtain the well posedness of smooth solution for the generalized navier stokes equations with initial data in some critical homogeneous besov type morrey spaces b p p 1 2 n 1 2 1 1 2 1 2 1 p 2 and n p 2 2 2 n p or 2 p and max n p 2 2 1 2 n p with divergence free these critical homogeneous besov type morrey spaces are larger than corresponding classical besov spaces and cover q spaces

carleson embeddings for sobolev spaces via heat equation abstract let u t x be the solution of the heat equation t x u t x 0 on r 1 n 0 r n subject to u 0 x f x on r n the main goal of this paper is to characterize such a nonnegative measure on r 1 n that f x u t 2 x induces a bounded embedding from the sobolev space w 1 p r n p 1 n into the lebesgue space l q r 1 n q 0

strong type estimates for homogeneous besov capacities capacitary strong type estimates for homogeneous besov spaces are established moreover the result is used to study embeddings and dualities of function spaces

asymptotic performance of linear receivers in mimo fading channels linear receivers are an attractive low complexity alternative to optimal processing for multiple antenna multiple input multiple output mimo communications in this paper we characterize the information theoretic performance of mimo linear receivers in two different asymptotic regimes for fixed number of antennas we investigate the limit of error probability in the high signal to noise ratio snr regime in terms of the diversity multiplexing tradeoff dmt following this we characterize the error probability for fixed snr in the regime of large but finite number of antennas as far as the dmt is concerned we report a negative result we show that both linear zero forcing zf and linear minimum mean square error mmse receivers achieve the same dmt which is largely suboptimal even in the case where outer coding and deacircnot coding is performed across the antennas we also provide an apacircnot proximate quantitative analysis of the markedly different behavior of the mmse and zf receivers at finite rate and nonasymptotic snr and show that while the zf receiver achieves poor diversity at any finite rate the mmse receiver error curve slope flattens out progressively as the coding rate increases when snr is fixed and the number of antennas becomes large we show that the mutual information at the output of an mmse or zf linear receiver has fluctuations that converge in distribution to a gaussian random variable whose mean and variance can be characterized in closed form this analysis extends to the linear reacircnot ceiver case a well known result previously obtained for the optimal receiver simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas

characterizations of weighted besov and triebel lizorkin spaces via temperatures abstract hardy littlewood type characterizations via temperatures on a half space of weighted besov and triebel lizorkin spaces studied recently by the author are given in the proof of the sufficient parts of the results a sub mean value property of temperatures is used in an elegant way to get control of certain terms by the hardy maximal function or its vector valued version as a byproduct of the results another characterization of weighted hardy spaces as well as characterizations of the gauss weierstrass integrals on a strip domain of distributions in the above weighted spaces is obtained also

linear multiuser receivers in random environments we study the signal to interference sir performance of linear multiuser receivers in random environments where signals from the users arrive in random directions such a random environment may arise in a ds cdma system with random signature sequences or in a system with antenna diversity where the randomness is due to channel fading assuming that such random directions can be tracked by the receiver the resulting sir performance is a function of the directions and therefore also random we study the asymptotic distribution of this random performance in the regime where both the number of users k and the number of degrees of freedom n in the system are large but keeping their ratio fixed our results show that for both the decorrelator and the minimum mean square error mmse receiver the variance of the sir distribution decreases like 1 n and the sir distribution is asymptotically gaussian we compute closed form expressions for the asymptotic means and variances for both receivers simulation results are presented to verify the accuracy of the asymptotic results for finite sized systems

new applications of besov type and triebel lizorkin type spaces abstract in this paper the authors prove that besov morrey spaces are proper subspaces of besov type spaces b p q s r n and that triebel lizorkin morrey spaces are special cases of triebel lizorkin type spaces f p q s r n the authors also establish an equivalent characterization of b p q s r n when 0 1 p these besov type spaces b p q s r n and triebel lizorkin type spaces f p q s r n were recently introduced to connect besov spaces and triebel lizorkin spaces with q spaces moreover for the spaces b p q s r n and f p q s r n the authors investigate their trace properties and the boundedness of the pseudo differential operators with homogeneous symbols in these spaces which generalize the corresponding classical results of jawerth and grafakos torres by taking 0

a john nirenberg type inequality for qα rn abstract the john nirenberg inequality characterizes functions in the space bmo in terms of the decay of the distribution function of their oscillations over a cube in this paper we prove separate necessary and sufficient john nirenberg type inequalities for functions in the space q r n introduced by essen janson peng and xiao who conjectured a version of this inequality our results are a modified version of their conjecture and we give a counterexample to show the necessity for this modification the counterexample also shows that these necessary and sufficient conditions cannot be reconciled

limit of the smallest eigenvalue of a large dimensional sample covariance matrix in this paper the authors show that the smallest if p leq n or the p n 1 th smallest if p n eigenvalue of a sample covariance matrix of the form 1 n xx tends almost surely to the limit 1 sqrt y 2 as n rightarrow infty and p n rightarrow y in 0 infty where x is a p times n matrix with iid entries with mean zero variance 1 and fourth moment finite also as a by product it is shown that the almost sure limit of the largest eigenvalue is 1 sqrt y 2 a known result obtained by yin bai and krishnaiah the present approach gives a unified treatment for both the extreme eigenvalues of large sample covariance matrices

solvability of multipoint boundary value problems at resonance for higher order ordinary differential equations let f 0 1 x r n r be a continuous function and e l 1 0 1 let b j 1 j m 2 r 0 h 1 h 2 h m 2 1 be given this paper is concerned with the existence of solutions for the following n t h order multipoint boundary value problems at resonance case x n t f t x t x t x n 1 t e t email protected 0 1 x 0 x 0 x n 2 0 0 x 1 email protected email protected jx h j and x n t f t x t x t x n 1 t e t email protected 0 1 x 0 x 0 x n 2 0 0 x 1 email protected email protected jx h j some existence results are obtained by using the coincidence degree theory of mawhin

random sequence multisets for synchronous code division multiple access channels the effect of using randomly selected sequence multisets for the uplink of a synchronous code division multiple access channel is considered a tight lower bound on the expected value of the sum capacity over the ensemble of randomly selected sequence multisets is given for large systems the sum rate penalty for using randomly selected multisets is shown to be at most 1 nat and to vanish as the number of users becomes large compared to the sequence length

sinr statistics of correlated mimo linear receivers linear receivers offer a low complexity option for multiantenna communication systems therefore understanding the outage behavior of the corresponding sinr is important in a fading mobile environment in this paper we introduce a large deviation method valid nominally for a large number m of antennas which provides the probability density of the sinr of gaussian channel mimo minimum mean square error mmse and zero forcing zf receivers with arbitrary transmission power profiles and in the presence of receiver antenna correlations this approach extends the gaussian approximation of the sinr valid for large m asymptotically close to the center of the distribution to obtain the non gaussian tails of the distribution our methodology allows us to calculate the sinr distribution to next to leading order o 1 m and showcase the deviations from approximations that have appeared in the literature e g the gaussian or the generalized gamma distribution we also analytically evaluate the outage probability as well as the uncoded bit error rate we find that our approximation is quite accurate even for the smallest antenna arrays 2 2

asymptotic normality of linear multiuser receiver outputs this paper proves large system asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers this family of receivers encompasses the single user matched filter the decorrelator the minimum mean square error mmse receiver the parallel interference cancelers and many other linear receivers of interest both with and without the assumption of perfect power control we show that the output decision statistic for each user converges to a gaussian random variable in distribution as the number of users and the spreading factor both tend to infinity with their ratio fixed analysis reveals that the distribution conditioned on almost all spreading sequences converges to the same distribution which is also the unconditional distribution this normality principle allows the system performance e g the multiuser efficiency to be completely determined by the output signal to interference ratio sir for large linear systems

mmse analysis of certain large isometric random precoded systems linear precoding consists in multiplying by an n spl times k matrix a k dimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted in this paper new tools borrowed from the so called free probability theory are introduced for the purpose of analyzing the performance of minimum mean square error mmse receivers for certain large random isometric precoded systems on fading channels the isometric condition represents the case of precoding matrices with orthonormal columns it is shown in this contribution that the signal to interference plus noise ratio sinr at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when n spl rarr spl infin and k n spl rarr spl alpha spl les 1 these asymptotic results are used to analyze the impact of orthogonal spreading as well as to optimally balance the redundancy introduced between linear precoding versus classical convolutional coding while preserving a simple mmse equalization scheme at the receiver

no eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices let b n 1 n t n 1 2 x n x n t n 1 2 where x n is n times n with i i d complex standardized entries having finite fourth moment and t n 1 2 is a hermitian square root of the nonnegative definite hermitian matrix t n it is known that as n to infty if n n converges to a positive number and the empirical distribution of the eigenvalues of t n converges to a proper probability distribution then the empirical distribution of the eigenvalues of b n converges a s to a nonrandom limit in this paper we prove that under certain conditions on the eigenvalues of t n for any closed interval outside the support of the limit with probability 1 there will be no eigenvalues in this interval for all n sufficiently large

hausdorff besov type and triebel lizorkin type spaces and their applications abstract let s r p 1 and 0 1 p where p denotes the conjugate index of p in this article the authors first introduce the hausdorff besov type space b h p q s r n with q 1 and the hausdorff triebel lizorkin type space f h p q s r n with q 1 via a class of weights defined on the upper plane and then establish some equivalent characterizations of b h p q s r n and f h p q s r n via some classes of weights defined on r n the authors then prove that their dual spaces are besov morrey and triebel lizorkin morrey spaces respectively the relations between these spaces and the known besov triebel lizorkin hausdorff spaces are also studied as an application for p 1 and 0 n the authors obtain the coincidence between the space f h p 2 0 n n p r n and the predual space h p r n of the morrey space l p r n moreover characterizations of b h p q s r n and f h p q s r n via local means and peetre maximal functions as well as the boundedness of riesz potential operators and some singular integrals on b h p q s r n and f h p q s r n are also obtained

existence and iteration of monotone positive solutions for multipoint boundary value problem with p laplacian operator in the paper we obtain the existence of monotone positive solutions and establish acorresponding iterative scheme for the following multipoint boundary value problem with p laplacian operator f p u t q t f t u t 0 0

q spaces and morrey spaces abstract we characterize functions in morrey space by p carleson measures we then reveal a simple relation between q space and morrey space that is q space can be viewed as a fractional integration of the morrey space therefore many results for morrey space can be translated onto q space for example we show that q space is a dual space by identifying its predual

new orlicz hardy spaces associated with divergence form elliptic operators abstract let l be the divergence form elliptic operator with complex bounded measurable coefficients the positive concave function on 0 of strictly critical lower type p 0 1 and t t 1 1 t 1 for t 0 in this paper the authors study the orlicz hardy space h l r n and its dual space bmo l r n where l denotes the adjoint operator of l in l 2 r n several characterizations of h l r n including the molecular characterization the lusin area function characterization and the maximal function characterization are established the carleson measure characterization and the john nirenberg inequality for the space bmo l r n are also given as applications the authors show that the riesz transform l 1 2 and the littlewood paley g function g l map h l r n continuously into l the authors further show that the riesz transform l 1 2 maps h l r n into the classical orlicz hardy space h r n for p n n 1 1 and the corresponding fractional integral l for certain 0 maps h l r n continuously into h l r n where is determined by and and satisfies the same property as all these results are new even when t t p for all t 0 and p 0 1

some results on q p spaces 0lpl1 for p is an element of 0 1 let q p be a proper subspace of bmoa defined by means of a modified garcia norm we give a boundary value criterion for a function to be in q p and a necessary and sufficient condition in terms of p carleson measure for an

decompositions of besov hausdorff and triebel lizorkin hausdorff spaces and their applications abstract let p 1 q 1 s r and 0 1 1 max p q in this paper the authors establish the transform characterizations of besov hausdorff spaces b h p q s r n and triebel lizorkin hausdorff spaces f h p q s r n q 1 as applications the authors then establish their embedding properties which on b h p q s r n is also sharp smooth atomic and molecular decomposition characterizations for suitable moreover using their atomic and molecular decomposition characterizations the authors investigate the trace properties and the boundedness of pseudo differential operators with homogeneous symbols in b h p q s r n and f h p q s r n q 1 which generalize the corresponding classical results on homogeneous besov and triebel lizorkin spaces when p 1 and q 1 by taking 0

fefferman stein decomposition for q spaces and micro local quantities abstract in this paper we study the fefferman stein decomposition of q r n and give an affirmative answer to an open problem posed by essen et al 2000 one of our main methods is to characterize the structure of the predual of q r n by the micro local quantities this result indicates that the norm of the predual space of q r n depends on the micro local structure in a self correlation way

on the relationship between mmse sic and bi gdfe receivers for large multiple input multiple output channels a minimum mean square error mmse based iterative soft interference cancellation mmse sic receiver has been proposed to mitigate the interferences of the multiple input multiple output mimo channels with reduced complexity as compared to maximum likelihood ml detection on the other hand the block iterative generalized decision feedback equalizer bi gdfe attains close to the performance of the mmse sic receivers with further reduced complexity the bi gdfe however requires an accurate estimate of the input decision correlation idc which is a statistical reliability metric of earlier made decisions to date the bi gdfe receiver is applicable only to phase shift keying psk modulations due to the absence of a method to estimate the idc for higher order quadrature amplitude modulations qams in this paper we establish the relationship between the mmse sic and bi gdfe receivers and propose an algorithm to determine the idc for bi gdfe from the unconditional mmse sic u mmse sic we further analyze and compare the asymptotic performances of the two receivers for large random mimo channels and prove that for the limiting case the output signal to interference plus noise ratios sinrs at each iteration for both receivers converge in probability to their respective deterministic limits our simulation results have shown that the bit error rate ber performance of the bi gdfe receiver with the proposed idc selection method achieves close to that of the u mmse sic receiver with similar convergence behavior and reaches the single user matched filter bound mfb with several iterations for high enough signal to noise ratio snr

a new class of function spaces connecting triebel lizorkin spaces and q spaces abstract let s r 0 p 1 and q 1 in this paper we introduce a new class of function spaces f p q s r n which unify and generalize the triebel lizorkin spaces with both p 1 and p and q spaces by establishing the carleson measure characterization of q space we then determine the relationship between triebel lizorkin spaces and q spaces which answers a question posed by dafni and xiao in g dafni j xiao some new tent spaces and duality theorem for fractional carleson measures and q r n j funct anal 208 2004 377 422 moreover via the hausdorff capacity we introduce a new class of tent spaces f t p q s r n 1 and determine their dual spaces f w p q s q r n where s r p q 1 max p q 1 0 q max p q and t denotes the conjugate index of t 1 as an application of this we further introduce certain hardy hausdorff spaces f h p q s r n and prove that the dual space of f h p q s r n is just f p q s q r n when p q 1

asymptotic performance of mmse receivers for large systems using random matrix theory random matrix theory is used to derive the limit and asymptotic distribution of signal to interference plus noise ratio sir for a class of suboptimal minimum mean square error mmse receivers applied to large random systems with unequal power users we prove that the limiting sir converges to a deterministic value when k and n go to infinity with lim k n y being a positive constant where k is the number of users and n is the number of degrees of freedom we also prove that the sir of each particular user is asymptotically gaussian for large n and derive the closed form expressions of the variance for the sir variable under real spreading and complex spreading channel environments it is revealed that for a given k n pair under certain mild conditions the variance of the sir for complex spreading channels is half of that for the corresponding real spreading channels since the suboptimal mmse receiver becomes optimal for the case when the users are equally powered our results show that the conjecture made by tse and zeitouni for the complex spreading case is not affirmative we also derive the asymptotic distribution for sir in decibels which provides better description when n is small numerical results and computer simulations are provided to evaluate the accuracy of various limiting and asymptotic results obtained in this paper

optimal l p l q estimates for parabolic boundary value problems with inhomogeneous data in this paper we investigate vector valued parabolic initial boundary value problems mathcal a t x d mathcal b j t x d subject to general boundary conditions in domains g in mathbb r n with compact c 2m boundary the top order coefficients of mathcal a are assumed to be continuous we characterize optimal l p l q regularity for the solution of such problems in terms of the data we also prove that the normal ellipticity condition on mathcal a and the lopatinskii shapiro condition on mathcal a mathcal b 1 dots mathcal b m are necessary for these l p l q estimates as a byproduct of the techniques being introduced we obtain new trace and extension results for sobolev spaces of mixed order and a characterization of triebel lizorkin spaces by boundary data

randomly spread cdma asymptotics via statistical physics this paper studies randomly spread code division multiple access cdma and multiuser detection in the large system limit using the replica method developed in statistical physics arbitrary input distributions and flat fading are considered a generic multiuser detector in the form of the posterior mean estimator is applied before single user decoding the generic detector can be particularized to the matched filter decorrelator linear minimum mean square error mmse detector the jointly or the individually optimal detector and others it is found that the detection output for each user although in general asymptotically non gaussian conditioned on the transmitted symbol converges as the number of users go to infinity to a deterministic function of a hidden gaussian statistic independent of the interferers thus the multiuser channel can be decoupled each user experiences an equivalent single user gaussian channel whose signal to noise ratio snr suffers a degradation due to the multiple access interference mai the uncoded error performance e g symbol error rate and the mutual information can then be fully characterized using the degradation factor also known as the multiuser efficiency which can be obtained by solving a pair of coupled fixed point equations identified in this paper based on a general linear vector channel model the results are also applicable to multiple input multiple output mimo channels such as in multiantenna systems

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

output mai distributions of linear mmse multiuser receivers in ds cdma systems multiple access interference mai in a code division multiple access cdma system plays an important role in performance analysis and characterization of fundamental system limits we study the behavior of the output mai of the minimum mean square error mmse receiver employed in the uplink of a direct sequence ds cdma system we focus on imperfect power controlled systems with random spreading and establish that in a synchronous system 1 the output mai of the mmse receiver is asymptotically gaussian and 2 for almost every realization of the signatures and received powers the conditional distribution of the output mai converges weakly to the same gaussian distribution as in the unconditional case we also extend our study to asynchronous systems and establish the gaussian nature of the output interference these results indicate that in a large system the output interference is approximately gaussian and the performance of the mmse receiver is robust to the randomness of the signatures and received powers the gaussianity justifies the use of single user gaussian codes for cdma systems with linear mmse receivers and implies that from the viewpoints of detection and channel capacity signal to interference ratio sir is the key parameter that governs the performance of the mmse receiver in a cdma system

consistent reduced rank lmmse estimation with a limited number of samples per observation dimension an improved construction of the optimal reduced rank linear minimum mean square error mmse estimator of a signal waveform of interest is derived that is consistent under a limited number of samples per filtering degree of freedom the new filter design generalizes traditional filter realizations based on directly replacing the theoretical covariance matrix by its sample estimate and being consistent when all dimensions in the model but the number of samples remain bounded our solution not only generalizes the conventional estimator but also turns out to appropriately characterize model mismatch constraints due to finite sample size limitations of fundamental importance in practical situations the proposed implementation results from a generalized consistent estimation of the set of mmse filter subspace coefficients on the reduced dimensional subspace results are based on the theory of the spectral analysis of large dimensional random matrices in particular we build on the analytical description of the asymptotic spectrum of sample covariance type matrices in the limiting regime defined as both the number of samples and the observation dimension grow without bound at the same rate as a result the proposed mmse signal waveform estimator is shown to present a superior mean square error performance under a finite sample size by avoiding the breakdown experienced as the selected rank increases

new besov type spaces and triebel lizorkin type spaces including q spaces let s tau in mathbb r and q in 0 infty we introduce besov type spaces dot b s tau p q mathbb r n for p in 0 infty and triebel lizorkin type spaces dot f s tau p q mathbb r n rm for p in 0 infty which unify and generalize the besov spaces triebel lizorkin spaces and q spaces we then establish the varphi transform characterization of these new spaces in the sense of frazier and jawerth using the varphi transform characterization of dot b s tau p q mathbb r n rm and dot f s tau p q mathbb r n we obtain their embedding and lifting properties moreover for appropriate we also establish the smooth atomic and molecular decomposition characterizations of dot b s tau p q mathbb r n rm and dot f s tau p q mathbb r n for s in mathbb r p in 1 infty q in 1 infty and tau in 0 frac 1 max p q via the hausdorff capacity we introduce certain hardy hausdorff spaces b dot h s tau p q mathbb r n and prove that the dual space of b dot h s tau p q mathbb r n is just dot b s tau p q mathbb r n where t denotes the conjugate index of t in 1 infty

homogeneous endpoint besov space embeddings by hausdorff capacity and heat equation two embeddings of a homogeneous endpoint besov space are established via the hausdorff capacity and the heat equation meanwhile a co capacity formula and a trace inequality are derived from the besov space

necessary and sufficient conditions for absolute continuity of elliptic harmonic measure our purpose in this paper is to give a necessary and sufficient condition on the modulus of continuity of the coefficients of an elliptic operator in divergence form in order that the corresponding poisson kernel for the dirichlet problem exist this condition on the coefficients is global continuity together with the additional property that the modulus of continuity along some nontangential direction at each boundary point be bounded uniformly in these points and directions by a function 7 t satisfying the dini type condition

iterative multiuser joint decoding optimal power allocation and low complexity implementation we consider a canonical model for coded code division multiple access cdma with random spreading where the receiver makes use of iterative belief propagation bp joint decoding we provide simple density evolution analysis in the large system limit large number of users of the performance of the bp decoder and of some suboptimal approximations based on interference cancellation ic based on this analysis we optimize the received user signal to noise ratio snr distribution in order to maximize the system spectral efficiency for given user channel codes channel load users per chip and target user bit error rate ber the optimization of the received snr distribution is obtained by solving a simple linear program and can be easily incorporated into practical power control algorithms remarkably under the optimized snr assignment the suboptimal minimum mean square error mmse ic based decoder performs almost as well as the more complex bp decoder moreover for a large class of commonly used convolutional codes we observe that the optimized snr distribution consists of a finite number of discrete snr levels based on this observation we provide a low complexity approximation of the mmse ic decoder that suffers from very small performance degradation while attaining considerable savings in complexity as by products of this work we obtain a closed form expression of the multiuser efficiency me of power mismatched mmse filters in the large system limit and we extend the analysis of the symbol by symbol maximum a posteriori probability map multiuser detector in the large system limit to the case of nonconstant user powers and nonuniform symbol prior probabilities

a statistical mechanics approach to large system analysis of cdma multiuser detectors we present a theory based on statistical mechanics to evaluate analytically the performance of uncoded fully synchronous randomly spread code division multiple access cdma multiuser detectors with additive white gaussian noise awgn channel under perfect power control and in the large system limit application of the replica method a tool developed in the literature of statistical mechanics allows us to derive analytical expressions for the bit error rate as well as the multiuser efficiency of the individually optimum io and jointly optimum jo multiuser detectors over the whole range of noise levels the information theoretic capacity of the randomly spread cdma channel and the performance of decorrelating and linear minimum mean square error mmse detectors are also derived in the same replica formulation thereby demonstrating validity of the statistical mechanical approach

on the limit of the largest eigenvalue of the large dimensional sample covariance matrix in this paper the authors show that the largest eigenvalue of the sample covariance matrix tends to a limit under certain conditions when both the number of variables and the sample size tend to infinity the above result is proved under the mild restriction that the fourth moment of the elements of the sample sums of squares and cross products sp matrix exist

well posedness and regularity of generalized navier stokes equations in some critical q spaces we study the well posedness and regularity of the generalized navier stokes equations with initial data in a new critical space q 1 rn q rn n 12 1 which is larger than some known critical homogeneous besov spaces here q rn is a space defined as the set of all measurable functions with sup l i 2 1 n i i f x f y 2 x y n 2 1 dxdy where the supremum is taken over all cubes i with edge length l i and edges parallel to the coordinate axes in rn in order to study the well posedness and regularity we give a carleson measure characterization of q rn by investigating a new type of tent spaces and an atomic decomposition of the predual for q rn in addition our regularity results apply to the incompressible navier stokes equations with initial data in q 1 1 rn

characterizations of besov type and triebel lizorkin type spaces via maximal functions and local means abstract let s r in this paper the authors first establish the maximal function characterizations of the besov type space b p q s r n with p q 0 and 0 the triebel lizorkin type space f p q s r n with p 0 q 0 and 0 the besov hausdorff space b h p q s r n with p 1 q 1 and 0 1 max p q and the triebel lizorkin hausdorff space f h p q s r n with p q 1 and 0 1 max p q where t denotes the conjugate index of t 1 using this characterization the authors further obtain the local mean characterizations of these function spaces via functions satisfying the tauberian condition and establish a fourier multiplier theorem on these spaces all these results generalize the existing classical results on besov and triebel lizorkin spaces by taking 0 and are also new even for q spaces and hardy hausdorff spaces

generalized poincare embeddings and weighted hardy operator on qpα q spaces abstract the poincare embeddings w 1 n r n bmo r n and the john nirenberg inequality in bmo r n are classical results in modern analysis and partial differential equations this paper studies the generalized poincare embeddings and the john nirenberg inequality in q p q r n spaces furthermore for the weighted hardy operator u and its adjoint v this paper gives sufficient and necessary conditions on weight function to ensure the boundedness of them on q p q r n spaces

the iterative solutions of 2nth order nonlinear multi point boundary value problems abstract the aim of this paper is to investigate the existence of iterative solutions for a class of 2 n th order nonlinear multi point boundary value problems the multi point boundary condition under consideration includes various commonly discussed boundary conditions such as three or four point boundary condition n 2 point boundary condition and 2 n m point boundary condition the existence problem is based on the method of upper and lower solutions and its associated monotone iterative technique a monotone iteration is developed so that the iterative sequence converges monotonically to a maximal solution or a minimal solution depending on whether the initial iteration is an upper solution or a lower solution two examples are presented to illustrate the results

asymptotic solutions for a second order differential equation with three point boundary conditions abstract in this paper we are concerned with the following singularly perturbed second order three point boundary value problem 1 1 y 2 q 1 x q 2 x y 0 1 1 2 y 0 a y 1 y where 0

some new tent spaces and duality theorems for fractional carleson measures and qα rn several duality questions for fractional carleson measures and the spaces q rn are resolved using a new type of tent spaces these tent spaces are defined in terms of choquet integrals with respect to hausdorff capacity a predual for q rn is then defined as a space of distributions containing the hardy space h1 and an atomic decomposition is proved

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

littlewood paley characterizations of triebel lizorkin morrey spaces via ball averages abstract let 1 p u and q 1 in this article the authors establish equivalent characterizations of the triebel lizorkin morrey space e u q p r n with smoothness order 0 2 in terms of the lusin area function and the g function generated by the difference between f x and its ball average b 2 j f x 1 b x 2 j b x 2 j f y d y j 1 2 x r n where for any j 1 2 and x r n b x 2 j y r n y x 2 j as applications the authors obtain several characterizations of e u p r n via pointwise inequalities involving ball averages

besov type spaces with variable smoothness and integrability abstract in this article the authors introduce besov type spaces with variable smoothness and integrability the authors then establish their characterizations respectively in terms of transforms in the sense of frazier and jawerth smooth atoms or peetre maximal functions as well as a sobolev type embedding as an application of their atomic characterization the authors obtain a trace theorem of these variable besov type spaces

generalized navier stokes equations with initial data in local q type spaces abstract in this paper we establish a link between leray mollified solutions of the three dimensional generalized navier stokes equations and mild solutions for initial data in the adherence of the test functions for the norm of q loc 1 r 3 this result applies to the usual incompressible navier stokes equations

greenʼs function for first order multipoint boundary value problems and applications to the existence of solutions with constant sign abstract we consider a first order linear differential equation subject to boundary value conditions which take into account the values of the function at multiple points in the interval of interest for this problem we calculate the green s function which allows to express in integral form the exact expression of the unique solution to the multipoint boundary value problem under the appropriate conditions from this study some results are derived concerning the existence of solutions with a constant sign that is some comparison results for first order multipoint boundary value problems