bmo spaces related to schrodinger operators with potentials satisfying a reverse holder inequality we identify the dual space of the hardy type space related to the time independent schrodinger operator v with v a potential satisfying a reverse holder inequality as a bmo type space we prove the boundedness in this space of the versions of some classical operators associated to hardy littlewood semigroup and poisson maximal functions square function fractional integral operator we also get a characterization of in terms of carlesson measures

counting dimensions of l harmonic functions in this article we will consider second order uniformly elliptic operators of divergence form defined on lri with measurable coefficients mainly we will give estimates on the dimension of space of solutions that grow at most polynomially of degree d more precisely in terms of a rectangular coordinate system xi n a second order uniformly elliptic operator of divergence form l acting on a function f e h c rin is given by

new abstract hardy spaces the aim of this paper is to propose an abstract construction of spaces which keep the main properties of the already known hardy spaces h1 we construct spaces through an atomic or molecular decomposition we prove some results about continuity from these spaces into l1 and some results about interpolation between these spaces and the lebesgue spaces we also obtain some results on weighted norm inequalities finally we present partial results in order to understand a characterization of the duals of hardy spaces

classes of hardy spaces associated with operators duality theorem and applications let l be the infinitesimal generator of an analytic semigroup on l 2 r n with suitable upper bounds on its heat kernels in auscher duong and mcintosh 2005 and duong and yan 2005 a hardy space h1 l r n and a bmo l r n space associated with the operator l were introduced and studied in this paper we define a class of h p l r n spaces associated with the operator l for a range of p 1 acting on certain spaces of morrey campanato functions defined in new morrey campanato spaces associated with operators and applications by duong and yan 2005 and they generalize the classical h p r n spaces we then establish a duality theorem between the h p l r n spaces and the morrey campanato spaces in that same paper as applications we obtain the boundedness of fractional integrals on h p l r n and give the inclusion between the classical h p r n spaces and the h p l r n spaces associated with operators

semigroup kernels poisson bounds and holomorphic functional calculus letlbe the generator of a continuous holomorphic semigroupswhose action is determined by an integral kernelkon a scale of spaceslp x under mild geometric assumptions on x we prove that iflhas a boundedh functional calculus onl2 x andksatisfies bounds typical for the poisson kernel thenlhas a boundedh functional calculus onlp x for eachp 1 moreover if x is of polynomial type andksatisfies second order gaussian bounds we establish criteria forlto have a bounded hormander functional calculus or a bounded davies helffer sjostrand functional calculus

maximal function characterizations for hardy spaces on spaces of homogeneous type with finite measure and applications abstract we prove nontangential and radial maximal function characterizations for hardy spaces associated to a non negative self adjoint operator satisfying gaussian estimates on a space of homogeneous type with finite measure this not only addresses an open point in the literature but also gives a complete answer to the question posed by coifman and weiss in the case of finite measure we then apply our results to give maximal function characterizations for hardy spaces associated to second order elliptic operators with neumann and dirichlet boundary conditions schrodinger operators with dirichlet boundary conditions and fourier bessel operators

boundedness of spectral multipliers of generalized laplacians on compact manifolds with boundary consider a second order strongly elliptic negative semidefinite differential operator l may be a system on a compact riemannian manifold overline m with smooth boundary where the domain of l is defined by a coercive boundary condition classically known results and also recent work in duong et al j funct anal 196 443 485 2002 and duong and mcintosh rev math iberoam 15 233 265 1999 establish sufficient conditions for l infty text bmo l continuity of varphi sqrt l where varphi in s 0 1 mathbb r and l is a suitable elliptic operator using a variant of the cheeger gromov taylor functional calculus due to mauceri et al math res lett 16 861 879 2009 and short time upper bounds on the integral kernel of e tl due to greiner arch ration mech anal 41 168 218 1971 we prove that a variant of such sufficient conditions holds for our operator l

duality of hardy and bmo spaces associated with operators with heat kernel bounds the introduction and development of hardy and bmo spaces on euclidean spaces r in the 1960s and 1970s played an important role in modern harmonic analysis and applications in partial differential equations these spaces were studied extensively in 32 22 18 19 31 and many others an l function f on r is in the hardy spaceh r if the area integral function of the poisson integral e t f satisfies

the solution of the kato square root problem for second order elliptic operators on rn we prove the kato conjecture for elliptic operators on jfin more precisely we establish that the domain of the square root of a uniformly complex elliptic operator l div av with bounded measurable coefficients in ietn is the

on fundamental solutions of generalized schrodinger operators abstract we consider the generalized schrodinger operator where is a nonnegative radon measure in r n n 3 assuming that satisfies certain scale invariant kato conditions and doubling conditions we establish the following bounds for the fundamental solution of in r n ce e 2 d x y x y n 2 x y ce e 1 d x y x y n 2 where d x y is the distance function for the modified agmon metric m x dx2 associated with we also study the boundedness of the corresponding riesz transforms 1 2 on lp r n dx

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

the use of fitted higher order polynomial coefficients as covariates in the analysis of growth curves summary for orthogonal polynomials fitted to repeated measurements a computer simulation study is used to investigate the effect of selecting higher order coefficients as covariates in order to minimise the estimated variance of lower order coefficients under the assumption that the repeated measurements have certain autoregressive covariance structures it is seen that the gain in precision due to covariance adjustment can be largely illusory and that the resulting estimates of variances can grossly underestimate the true variances the consequences of using all higher order coefficients as covariates is also examined and seen to produce a gain in precision in certain circumstances in this paper we consider a particular approach to the analysis of data from repeated measurements experiments i e those in which a sequence of measurements of the same variable is taken from each experimental unit such experiments are commonly used for comparing the growth rates of organisms there are difficulties in the analysis of repeated measurements data due to the impossibility of randomly allocating time points which means that the assumptions of homogeneity of variance and uniform within unit correlation frequently do not hold we are concerned here with examples in which no theoretically based mathematical model is available to explain the observed response over time but in which the response can be adequately summarized by a polynomial of low degree wishart 1938 showed in the context of growth rate comparison how most of the difficulties can then be conveniently avoided by fitting the low degree polynomial to the repeated measurements from each unit and basing subsequent analysis on the fitted coefficients the analysis of the linear coefficients provides a comparison of average growth rate that of the quadratic coefficients a comparison of rate of change of growth rate and so on however in this process the information in the fitted higher order coefficients which do not show treatment differences is discarded in an attempt to make use of this information some or all of these higher order coefficients can be used as covariates a possibility first mentioned by leech and healy 1959 much of the theoretical groundwork for this approach was laid by rao 1965 1966 1967 in a multivariate context and an exposition of the technique is given by grizzle and allen 1969 one of the main problems in the approach lies in the choice of which covariates to use the use of all the covariates corresponds under normality to maximum likelihood estimation but it can easily be shown that this is sometimes very inefficient the selection of only those covariates that contribute significantly or to any extent to the precision is tempting but is likely to lead to an overestimate of this precision it can be argued that this is no different from the problem of covariate selection in standard analysis of covariance however in the present situation the potential covariates are transformed

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

new function spaces of bmo type the john nirenberg inequality interpolation and applications in this paper we introduce and develop some new function spaces of bmo bounded mean oscillation type on spaces of homogeneous type or measurable subsets of spaces of homogeneous type the new function spaces are defined by variants of maximal functions associated with generalized approximations to the identity and they generalize the classical bmo space we show that the john nirenberg inequality holds on these spaces and they interpolate with lp spaces by the complex interpolation method we then give applications on lp boundedness of singular integrals whose kernels do not satisfy the hormander condition 2005 wiley periodicals inc

noncommutative riesz transforms a probabilistic approach for 2 p 0 in the classical setting this is certainly satisfied for the maps tt f f 1 t where t is a semigroup of measure preserving maps on a probability space in that case n l then the maps tt act on all noncommutative lp spaces lp n and in particular on the hilbert space l2 l2 n let a be the negative generator i e tt e ta for technical reasons we have to assume that there is a weakly dense algebra a n which lies in the domain of the unbounded operator a i e a a a the algebra a plays the role of smooth functions in the classical setting this assumption might be too restrictive for some classical applications but it is easily verified in the new noncommutative examples for elements x y a we may define the gradient form 2 x y a x y x a y a x y the correct definition of is the one given by sauvageot as a bilinear form with values in l1 again our arguments require stronger assumptions in fact in all our examples we will assume that the tt s are selfadjoint i e ttxy xtty and unital i e tt 1 1 then a is indeed a positive unbounded operator under these circumstances we can formulate p a meyer s problem is it true that x x 2 p c p a 1 2 x p 0 1 holds for all selfadjoint elements x a let us illustrate this question by considering the laplace operator a f f where i 2 x2 i then it is easily verified that

regularity properties of the heat kernel and area integral characterization of hardy space hl1 related to degenerate schrodinger operators abstract in this paper we introduce the area integral associated with the heat semigroup t t t 0 generated by a degenerate schrodinger operator l we obtain a regularity estimate of the kernels of the semigroup t t t 0 this regularity together with a reproducing formula enables us to establish the area integral characterization of the hardy space associated with l

littlewood paley functions associated to second order elliptic operators we prove l p estimates for the littlewood paley function associated with a second order divergence form operator l div a with bounded measurable complex coefficients in n

zeta functions of line middle total graphs of a graph and their coverings we consider the ihara zeta functions of line graphs middle graphs and total graphs of a regular graph and their regular or irregular covering graphs let l g m g and t g denote the line middle and total graph of g respectively we show that the line middle and total graph of a regular and irregular respectively covering of a graph g is a regular and irregular respectively covering of l g m g and t g respectively for a regular graph g we express the zeta functions of the line middle and total graph of any regular or irregular covering of g in terms of the characteristic polynomial of the covering also the complexities of the line middle and total graph of any regular or irregular covering of g are computed furthermore we discuss the l functions of the line middle and total graph of a regular graph g