on a theorem of muckenhoupt and wheeden and a weighted inequality related to schrodinger operators we extend in several directions a theorem of b muckenhoupt and r wheeden relating the l p norms of riesz potentials and fractional maximal operators we apply these results to give a simple proof and sharpen a weighted inequality for schrodinger operators of chang wilson and wolff

estimation of variance of the regression estimator abstract the regression estimator and the ratio estimator are commonly used in survey practice in the past more attention has been given to the ratio estimator because of its computational ease and applicability for general sampling designs the ratio estimator is appropriate for populations whose regression line passes close to the origin if the intercept of the regression line is significantly nonzero however it is much less efficient than the regression estimator deng 1984 in general apart from n 2 terms the mean squared error mse of the former is bigger than that of the latter cochran 1977 p 196 given the present computing capacity the computational advantage of the ratio estimator should be less of a concern and the regression estimator will gain wider popularity the main purpose of this article is to provide a theoretical and empirical comparison of several variance estimators for the regression estimator in simple random sampling without replacement the companion problem for the

a generalization of the carleson lemma and weighted norm inequalities for the maximal functions in the orlicz setting abstract in this note we introduce the notion of carleson sequence for a convex growth function and provide an equivalent characterization that is an extension of the off diagonal carleson embedding lemma we apply this result to obtain sawyer type characterization and two weight norm estimates for some maximal functions between different orlicz spaces

weighted norm inequalities for oscillatory integrals with finite type phases on the line abstract we obtain two weighted l 2 norm inequalities for oscillatory integral operators of convolution type on the line whose phases are of finite type the conditions imposed on the weights involve geometrically defined maximal functions and the inequalities are best possible in the sense that they imply the full l p r l q r mapping properties of the oscillatory integrals our results build on work of carbery soria vargas and the first author

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

sharp two weight inequalities for singular integrals with applications to the hilbert transform and the sarason conjecture abstract we prove two weight norm inequalities for calderon zygmund singular integrals that are sharp for the hilbert transform and for the riesz transforms in addition we give results for the dyadic square function and for commutators of singular integrals as an application we give new results for the sarason conjecture on the product of unbounded toeplitz operators on hardy spaces

weighted norm inequalities for potentials with applications to schrodinger operators fourier transforms and carleson measures on donne une nouvelle caracterisation de l inegalite de trace pour des operateurs potentiel et on l utilise pour affiner des resultats sur la distribution des valeurs propres des operateurs de schrodinger

sharp weighted norm inequalities for littlewood paley operators and singular integrals abstract we prove sharp l p w norm inequalities for the intrinsic square function introduced recently by m wilson in terms of the a p characteristic of w for all 1 p this implies the same sharp inequalities for the classical lusin area integral s f the littlewood paley g function and their continuous analogs s and g also as a corollary we obtain sharp weighted inequalities for any convolution calderon zygmund operator for all 1 p 3 2 and 3 p and for its maximal truncations for 3 p

efficient estimation of quadratic finite population functions in the presence of auxiliary information by viewing quadratic and other second order finite population functions as totals or means over a derived synthetic finite population we show that the recently proposed model calibration and pseudoempirical likelihood methods for effective use of auxiliary information from survey data can be readily extended to obtain efficient estimators of quadratic and other second order finite population functions in particular estimation of a finite population variance covariance or variance of a linear estimator can be greatly improved when auxiliary information is available the proposed methods are model assisted in that the resulting estimators are asymptotically design unbiased irrespective of the correctness of a working model but very efficient if the working model is nearly correct they have a number of attractive features which include applicability to a general sampling design incorporation of information on possibly multivariate auxiliary variables and the ability to entertain linear or nonlinear

weighted norm inequalities for the continuous square function we prove new weighted norm inequalities for real variable analogues of the lusin area function we apply our results to obtain new i weighted norm inequalities for singular integral operators ii weighted sobolev inequalities iii eigenvalue estimates for degenerate schrodinger operators

two weight extrapolation via the maximal operator abstract we give several extrapolation theorems for pairs of weights of the form w m k w and w mw w r w where w is any non negative function r 1 and m k is the k th iterate of the hardy littlewood maximal operator as an application we show that our results can be used to extend and sharpen results for square functions and singular integral operators by chang et al 1985 comment math helv 60 217 246 chanillo and wheeden 1987 indiana univ math j 36 277 294 wilson 1987 duke math j 55 879 887 1989 trans amer math soc 314 661 692 1989 illinois j math 33 361 366 and uchiyama 1995 studia math 115 135 149 in the process we prove a conjecture due to wilson

le complexe de chaines d un g complexe simplicial acyclique resume let g be a finite group the main result of this note shows that the reduced chain complex of an acyclic finite dimensional simplicial g complex is a split acyclic complex of z g modules the proof requires the extension of well known results on finitely generated p permutation modules to arbitrary p permutation modules the key is a theorem stating that a bounded complex of p permutation modules is split acyclic if and only if all its brauer quotients are acyclic

multiparameter operators and sharp weighted inequalities this article is concerned with the operators from harmonic analysis which are naturally associated to a multiple parameter family of dilations we are especially interested here in dealing with questions from the theory of such operators whose answers cannot be obtained by a reduction to the case of product operators we also introduce a new tool in order to carry out this multiparameter analysis which comes from the classical theory this is the concept of sharp weighted inequalities where for operators such as the hilbert transform or classical square function one asks for hilbert space inequalities which imply the correct estimates of the norm on lp of these operators as p becomes large 0 introduction in this article our main goal is to study classes of oper ators associated with multiparameter groups of dilations on rn in some sense the consideration of these operators is a natural next step or simplest case after those of the classical calderon zygmund theory and the product space theory it turns out that in order to obtain estimates for the multiparameter operators we shall be led to the following type of extremely classical question how does one obtain l2 estimates on r1 for the hilbert transform or other singular integrals which yield sharp estimates on the lp rl operator norm of h as p approaches 1 or oc these sharp weighted inequalities are of some independent interest and their study will be seen to be essentially equivalent to the deep work of chang wilson and wolff 3 on the exponential square integrability of functions whose area integral is bounded they also have other applications for example they provide an immediate extension of the chang wilson wolff estimates to product spaces as given by pipher in 12 at this point let us be more specific about the exact nature of the multipa rameter operators which we shall consider consider in r3 the dilations given by ps t x y z sx ty9 stz for s91 0 then there is a maximal operator first considered by zygmund ml and singular integrals tl introduced by ricci and stein 13 naturally associated to these dilations the maximal operator af3 is defined by

conditional coverage properties of finite population confidence intervals abstract standardized errors t v 1 2 were calculated for both ratio and regression estimators in each of 10 000 simple random samples of n 32 from each of six populations using four different variance estimators graphs show how the percentage of intervals t 1 96 v 1 2 that fail to contain t changes as a function of the average value of the auxiliary variable in the sample they reveal that a intervals using the variance estimators from standard linear regression theory were hopelessly unreliable b intervals using the conventional finite population variance estimators showed a striking excess of failures in badly balanced samples and c none of the four variance estimators produced satisfactory confidence intervals in populations arising from badly skewed prediction models

weighted estimates for conic fourier multipliers we prove a weighted inequality which controls conic fourier multiplier operators in terms of lacunary directional maximal operators by bounding the maximal operators this enables us to conclude that the multiplier operators are bounded on l p mathbb r 3 with 1 p infty

the weighted residual technique for estimating the variance of the general regression estimator of the finite population total summary the paper deals with design based estimation of the variance of the general regression estimator of the finite population total the usual taylor linearization variance estimator is an expression in the design weighted regression residuals in many applications the resulting expression is counterintuitive from a model based standpoint the improved variance estimator in this paper attaches another simple weight called g weight to each individual residual this new variance estimator i gives valid design based confidence intervals ii is nearly unbiased uiider a suitably chosen regression model and iii works well for conditional inference examples are given

finiteness properties for subgroups of gl n mathbb z abstract we construct finitely presented subgroups of gl n mathbb z that have infinitely many conjugacy classes of finite subgroups this answers a question of grunewald and platonov we suggest a variation on their question

the spectrum of the schrodinger operator on decrit le spectre negatif de l operateur de schrodinger avec un potentiel singulier on determine la valeur exacte du fond du spectre et on etablit une double estimation

morse theory and finiteness properties of groups we examine the finiteness properties of certain subgroups of right angled artin groups in particular we find an example of a group that is of type fp z but is not finitely presented

cohomological finiteness conditions for mackey and cohomological mackey functors abstract we study cohomological finiteness conditions for groups associated to mackey and cohomological mackey functors proving that the cohomological dimension associated to cohomological mackey functors is always equal to the f cohomological dimension and characterising the conditions mackey fp n and cohomological mackey fp n

harmonic analysis on product spaces rn x r and commute with the dilations p33 8 x2 x2 61x1 62x2 for x1 e rn x2 e rm and 61 82 0 then the corresponding operators are related to many problems in the theory of multiple fourier integrals see zygmund 21 the maximal operator which commutes with the p31382 is the jessen marcinkiewicz and zygmund 14 strong maximal operator ms defined by 1 ms f x1 x2 sup ri a y1 y2 1 dy1 dy2 xl x2 gr jr1

precision estimation in sample survey inference a criterion for choice between variance estimators summary we advocate the mean squared error of predicted squared error as a universal criterion for the choice between variance estimators in sample survey inference the predictive nature of the measure rewards variance estimators adapted to the amount of information in the actual sample this makes the new measure more satisfactory than the simpler mean squared error of the variance estimator the criterion turns out to be the same for design based as for model based inference and may also be used for comparison between the design and model based theoretical variances the theory is exemplified for the ratio estimator by a study of six variance estimators suggested in the literature these calculations are primarily made under a proportional regression model but consideration is also paid to model robustness three of the six estimators are shown to be inferior to the three others which are approximately equivalent

lack of natural weighted estimates for some singular integral operators we show that the classical hormander condition or analogously the l r hormander condition for singular integral operators t is not sufficient to derive coifman s inequality rn tf x p w x dx c rn mf x p w x dx where 0 p m is the hardy littlewood maximal operator w is any a weight and c is a constant depending upon p and the a constant of w this estimate is well known to hold when t is a calderon zygmlmd operator as a consequence we deduce that the following estimate does not hold rn t f x p w x dx c rn mf x p mw x dx where 0 p 1 and where w is an arbitrary weight however by a recent result due to a lerner this inequality is satisfied whenever t is a calderon zygmund operator one of the main ingredients of the proof is a very general extrapolation theorem for a weights

subdyadic square functions and applications to weighted harmonic analysis abstract through the study of novel variants of the classical littlewood paley stein g functions we obtain pointwise estimates for broad classes of highly singular fourier multipliers on r d satisfying regularity hypotheses adapted to fine subdyadic scales in particular this allows us to efficiently bound such multipliers by geometrically defined maximal operators via general weighted l 2 inequalities in the spirit of a well known conjecture of stein our framework applies to solution operators for dispersive pde such as the time dependent free schrodinger equation and other highly oscillatory convolution operators that fall well beyond the scope of the calderon zygmund theory

paraproducts and the exponential square class we prove that if a locally integrable f has a pointwise bounded dyadic square function where the square function is defined with respect to a so called accretive weight b t hen f is locally exponentially square integrable we generalize the result to d dimensions by means of canonical haar functions for l 2 r d 2002 elsevier science usa all rights reserved

a stein conjecture for the circle we discuss the manner in which one might expect directional maximal functions to control the fourier extension operator via l 2 weighted inequalities we prove a general inequality of this type for the extension operator restricted to circles in the plane

mixed a1 a bounds for fractional integrals abstract for a fractional integral operator i we show that i f l q w q c w a q 1 p w a 1 q 1 q f l p w p where w a q sup q 1 w q q q m q w q d x is wilson a q s constant which is smaller than the a 1 q constant we also prove a weak type 1 1 bound for a couple of weights of the form w m w assuming that w a

hardy space estimates for limited ranges of muckenhoupt weights abstract in this article we give a full necessary and sufficient set of conditions for a calderon zygmund operator to be bounded on weighted hardy spaces h w p where w is an muckenhoupt weight and 0 p in fact this result is new even when 1 p since it allows for h w p boundedness of an operator when 1 p q and w a q where it is possible that h w p l w p these singular integral results are achieved by proving littlewood paley stein square function type estimates from h w p into l w p for 0 p and a muckenhoupt weight w which are interesting results in their own right new techniques involving a weight invariant spaces are also used to prove the weighted estimates for calderon zygmund operators more precisely we prove the following bmo type weight invariance properties for a fixed s 0 the weighted sobolev bmo spaces i s b m o w coincide for all w a the weighted p type triebel lizorkin spaces f w s 2 coincide for all w a and these two classes of spaces coincide with each other as well all of which have comparable norms up to constants depending on an a p character of the weight w a

weighted lp estimates for the area integral associated with self adjoint operators on homogeneous space abstract let x be a metric space with doubling measure and l be a non negative self adjoint operator such that the corresponding heat kernels satisfy gaussian bounds this article is concerned with some weighted norm inequalities for area integrals associated with l as an application we obtain sharp estimates for the operator norm of the area integrals on l p x as p becomes large

weighted rearrangement inequalities for local sharp maximal functions several weighted rearrangement inequalities for uncentered and centered local sharp functions are proved these results are applied to obtain new weighted weak type and strong type estimates for singular integrals a self improving property of sharp function inequalities is established

sharp bound of the maximal bochner riesz operator in weighted lebesgue spaces abstract we study the bochner riesz operator on weighted lebesgue spaces and give the sharp bound for the maximal bochner riesz operator in terms of the a p characteristic of the weight function for 1 p 3

estimation of variance of the ratio estimator summary a general class of estimators of the variance of the ratio estimator is considered which includes two standard estimators vo and v2 and approximates another estimator vh suggested by royall eberhardt 1975 asymptotic expansions for the variances and biases of the proposed estimators are obtained based on this we obtain optimal variance estimators in the class and compare the relative merits of three estimators vo v1 and v2 without any model assumption under a simple regression model a more definite comparison of vo v1 and v2 is made in terms of variance and bias some key word8 asymptotic expansion bias optimal variance estimator ratio estimator superpopulation variance

euler classes and bredon cohomology for groups with restricted families of finite subgroups we explore some of the special features with respect to bredon cohomology for groups whose finite subgroups are all either nilpotent or p groups or cyclic p groups we get some results on dimensions and also a formula for the equivariant euler class for certain groups we consider the generalization for bredon cohomology of the properties of being duality or poincare duality and study their behavior under p power index extensions with coefficients in a field of characteristic p

the finite population linear regression estimator and estimators of its variance an empirical study abstract the usual variance estimator for the linear regression estimator of a finite population total is examined under some prediction superpopulation models its bias is compared with that of the least squares variance estimator also described are three bias robust alternatives one of which is the jackknife variance estimator the theoretical results are supported by an empirical study in which simple and restricted random samples as well as some purposive nonrandom samples are drawn from six real populations the results illustrate the need for prediction models and the inadequacy of randomization per se in providing a theoretical framework for robust inferences

erratum to weighted norm inequalities for the continuous square function trans amer math soc 314 1989 no 2 661 692 mr0972707 91e 42025

cohomological finiteness conditions for elementary amenable groups it is proved that every elementary amenable group of type fp admits a cocompact classifying space for proper actions

sharp weighted inequalities for the vector valued maximal function we prove in this paper some sharp weighted inequalities for the vector valued maximal function mq of fefferman and stein defined by 00 llq mqf x mfi o q where m is the hardy littlewood maximal function as a consequence we derive the main result establishing that in the range 1 a jf x jq mw x dx a rn where c is a constant independent of a 1 motivation and description of the main results the purpose of this paper is to obtain some sharp weighted inequalities for the vector valued maximal function mq which are not within the scope of the standard ap theory for vector valued singular integrals as can be found in rrt we start with a review of some of the classical estimates and then we shall state the main results 1 1 background let m be the hardy littlewood maximal function and let mq be the vector valued maximal operator defined by mq f x e m fi x q this nonlinear operator was introduced by c fefferman and e m stein in fs as a generalization of both the scalar maximal function m and the classical integral of marcinkiewicz and since then it has played an important role in the development of modern harmonic analysis we recall the two basic estimates obtained in fs for 1 q oo received by the editors may 19 1997 1991 mathematics subject classification primary 42b20 42b25 42b15 this work was partially supported by dgicyt grant pb940192 spain 2000 american mathematical society 3265 this content downloaded from 207 46 13 102 on sat 30 jul 2016 04 48 12 utc all use subject to http about jstor org terms

generalized hormander s conditions commutators and weights we present a general framework to deal with commutators of singular integral operators with bmo functions hormander type conditions associated with young functions are assumed on the kernels coifman type estimates weighted norm inequalities and two weight estimates are considered we give applications to homogeneous singular integrals fourier multipliers and one sided operators

entropy determinants and l 2 torsion we show that for any amenable group and any z module m of type fl with vanishing euler characteristic the entropy of the natural action on the pontryagin dual of m is equal to the l 2 torsion of m as a particular case the entropy of the principal algebraic action associated with the module z z f is equal to the logarithm of the fuglede kadison determinant of f whenever f is a non zero divisor in z this conrms a conjecture of deninger as a key step in the proof we provide a general szeg o type approximation theorem for the fuglede kadison determinant on the group von neumann algebra of an amenable group as a consequence of the equality between l 2 torsion and entropy we show that the l 2 torsion of a non trivial amenable group with nite classifying space vanishes this was conjectured by luck finally we establish a milnor turaev formula for the l 2 torsion of a nite acyclic chain complex

subgroups of graph groups given a graph x we define a group gx as follows gx is generated by the vertices of x with a defining relation xy jt for each pair y 2 of ver tices joined by an edge of x a group is called a graph group if it is isomorphic to gx for some graph x we will not distinguish by notation in what follows between a vertex of x and the corresponding element of gx we remark that the extreme cases of graphs namely the complete and the completely disconnected graphs correspond respectively to free abelian and free groups it is well known that any subgroup of a group of either of these types is again of the same type and it is thus natural to ask to what extent and in what form this is true of the graph groups that lie in between these extreme cases in this article we will prove the following

on some sharp weighted norm inequalities abstract given a weight we consider the space ml p which coincides with l p when a p sharp weighted norm inequalities on ml p for the calderon zygmund and littlewood paley operators are obtained in terms of the a p characteristic of for any 1 p

on asymptotically design unbiased estimators of a finite population mean summary certain regression type estimators of a finite population mean are examined for their asymptotic design properties a sufficient condition that implies the design consistency or asymptotic design unbiasedness is discussed for a general regression estimator the leading term of its asymptotic bias is explicitly derived when this condition holds as well as when it does not hold

dimension of elementary amenable groups this paper has three parts it is conjectured that for every elementary amenable group g and every non zero commutative ring k the homological dimension hdk g is equal to the hirsch length h g whenever g has no k torsion in part i this conjecture is proved for several classes including the abelian by polycyclic groups in part ii it is shown that the elementary amenable groups of homological dimension one are colimits of systems of groups of cohomological dimension one in part iii the deep problem of calculating the cohomological dimension of elementary amenable groups is tackled with particular emphasis on the nilpotent by polycyclic case where a complete answer is obtained over q for countable groups

on the failure of lower square function estimates in the non homogeneous weighted setting we show that the classical a infty condition is not sufficient for a lower square function estimate in the non homogeneous weighted l 2 space we also show that under the martingale a 2 condition an estimate holds true but the optimal power of the characteristic jumps from 1 2 to 1 even when considering the classical a 2 characteristic this is in a sharp contrast to known estimates in the dyadic homogeneous setting as well as the recent positive results in this direction on the discrete time non homogeneous martingale transforms last we give a sharp a infty estimate for the n adic homogeneous case growing with n

some groups of type vf a group is of type vf if it contains a finite index subgroup which has a finite classifying space we construct groups of type vf in which the centralizers of some elements of finite order are not of type vf and groups of type vf containing infinitely many conjugacy classes of finite subgroups from these examples it follows that a group g of type vf need not admit a finite type or finite classifying space for proper actions sometimes also called the universal proper g space we construct groups g for which the minimal dimension of a universal proper g space is strictly greater than the virtual cohomological dimension of g each of our groups embeds in some general linear group over the rational integers applications to algebraic k theory of group algebras and topological k theory of group c algebras are also considered the groups are constructed as finite extensions of bestvina brady groups