generalized weighted hardy cesaro operators and their commutators on weighted morrey spaces abstract let 0 1 0 s 0 1 r be measurable functions and be a parameter curve in r n given by t x 0 1 r n s t x s t x in this paper we study a new weighted hardy cesaro operator defined by u s f x 0 1 f s t x t d t for measurable complex valued functions f on r n under certain conditions on s t and on an absolutely homogeneous weight function we characterize the weight function such that u s is bounded on weighted morrey spaces l p and then compute the corresponding operator norm of u s we also give a necessary and sufficient condition on the function which ensures the boundedness of the commutator of the operator u s on l p with symbols in bmo

convergence theorems for strongly pseudo contractive and strongly accretive maps supposeeis an arbitrary real banach space andkis a nonempty closed convex and bounded subset ofe supposet k kis a uniformly continuous strong pseudo contraction with constantk 0 1 suppose an bn cn a n b n and c n are sequences in 0 1 satisfying the following conditions i an bn cn 1 a n b n c n integersn 0 ii lim bn lim b n lim c n 0 iii bn iv cn for arbitraryx0 u0 v0 k define the sequence xn n 0iteratively byxn 1 anxn bntyn cnun yn a nxn b ntxn c nvn n 0 where un vn are arbitrary sequences ink then xn converges strongly to the unique fixed point oft related results deal with the iterative solutions of nonlinear equations involving set valued strongly accretive operators

the norm inequalities for the weighted cesaro mean operators this paper gives some necessary and sufficient conditions for the weighted cesaro mean operators to be bounded on herz spaces the corresponding new operator norm inequalities are obtained

hyperbolic cone manifolds short geodesics and schwarzian derivatives given a geometrically finite hyperbolic cone manifold with the cone singularity sufficiently short we construct a one parameter family of cone manifolds decreasing the cone angle to zero we also control the geometry of this one parameter family via the schwarzian derivative of the projective boundary and the length of closed geodesics

lp and bmo bounds of weighted hardy littlewood averages abstract this paper characterizes those nonnegative functions defined on 0 1 for which the weighted hardy littlewood average u f 0 1 f t t dt is bounded on either l p r n p 1 or bmo r n meanwhile the corresponding operator norms are worked out

iterative process with errors of nonlinear equations involvingm accretive operators abstract let x be a uniformly smooth and uniformly convex banach space and t d t x x be an m accretive operator with the domain d t and the range r t for any given f x we prove that the mann and ishikawa type iterative sequences with errors converge strongly to the unique solution of the equation x tx f where t may not be lipschitz some related results deal with the convergence of mann and ishikawa type iterative sequences with errors for approximating a solution of a continuous dissipative operator equation

iterative solutions of nonlinear accretive operator equations in arbitrary banach spaces suppose e is an arbitrary real banach space and k is a nonempty closed convex and bounded subset of e suppose t k k is a uniformly continuous strong pseudocontraction it is proved that the mann and the ishikawa iteration methods converge strongly to the unique fixed point of t furthermore our results also hold for the slightly more general class of strictly hemicontractive maps related results deal with the iterative approximation of solutions of accretive operator equations in arbitrary real banach spaces miramare trieste april 1996 permanent address department of mathematics university of nigeria nsukka nigeria

iterative processes with mixed errors for nonlinear equations with perturbed m accretive operators in banach spaces let x be a real uniformly smooth banach space of which the dual x has a frechet differentiable norm let a d a x 2 x be an m accretive operator with closed domain d a and bounded range r a and s x x a continuous and a strongly accretive operator with bounded range r i s it is proved that the ishikawa and mann iterative processes with mixed errors converge strongly to the unique solution of the equation z sx lax for given z x and l 0

convergence of iterative processes with errors for set valued pseudocontractive and accretive type mappings in banach spaces abstract in this paper some new results on convergence of iterative processes with errors for set valued pseudocontractive and accretive mappings in banach spaces are obtained our results extend and improve a number of the recent results

continuity of hardy type operators on rectangularly defined spaces abstract we introduce a generalization of rectangular herz spaces defined in 3 and prove boundedness of a version of the n dimensional hardy operator on them we also study the action of the hausdorff operator on some subspaces of bmo

critical differentiability of maps and canceling operators for a first order homogeneous linear differential operator mathbb a and 1 q infty we show that l n n 1 q differentiability of bv mathbb a text loc maps is equivalent to van schaftingen s elliptic and canceling ec condition for mathbb a for higher order ec operators we give a generalization of dorronsoro s theorem on critical l p taylor expansions for bv k maps here bv mathbb a text loc is the space of u in l 1 text loc such that mathbb a u is a radon measure these results can be formulated as sharp pointwise regularity results for elliptic systems mathbb a u mu where mu is a radon measure thereby covering the limiting case p 1 of a theorem of calder on and zygmund which was open so far

approximating solutions for the systems of strongly accretive operator equations the purpose of this paper is to study a strong convergence of multi step iterative scheme to a common fixed point for a finite family of strongly pseudo contractive mappings as a consequence the strong convergence theorems for the modified multi step iterative sequence to a solution of systems of strongly accretive operator equations are obtained in real uniformly smooth banach spaces the results presented in this paper improve and extend the corresponding xu y xu ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations j math anal appl 224 1998 91 101 and noor rassias and huang m a noor t m rassias z huang three step iterations for nonlinear accretive operator equations j math anal appl 274 2002 59 68 and many others

description of all conformally invariant differential operators acting on scalar functions we present an algorithm to obtain all conformally invariant differential operators acting on scalar functions and taking values on scalar functions as well there are two cases under consideration operators acting on functions defined on the euclidean space r4 and on the minkowski space in both cases each conformally invariant operator of order k is nonlinear and is a function of a finite set of functionally independent invariant operators of order up to k in particular the second order independent operators are only three and we give their explicit realization the applied technique is based on the jet bundle formalism analysis of the group action and a dimensional reduction as a simple illustration of this method we consider the case of differential operators between analytic functions on c which are invariant under the action of the modular group a power series which generates all functionally independent invariant operators is derived

the solution by iteration of nonlinear equations in uniformly smooth banach spaces abstract letebe a uniformly smooth banach space and lett d t e ebe a strong pseudocontraction with an open domaind t ineand a fixed pointx d t we establish the strong convergence of the mann and ishikawa iterative processes with errors to the fixed point oft related results deal with the iterative solution of operator equations of the formsf txandf x tx 0 whentis a set valued strongly accretative operator our theorems include the cases in which the operatortis defined only locally explicit error estimates are also given

conformally invariant powers of the laplacian q curvature and tractor calculus we describe an elementary algorithm for expressing as explicit formulae in tractor calculus the conformally invariant gjms operators due to c r graham et alia these differential operators have leading part a power of the laplacian conformal tractor calculus is the natural induced bundle calculus associated to the conformal cartan connection applications discussed include standard formulae for these operators in terms of the levi civita connection and its curvature and a direct definition and formula for t branson s so called q curvature which integrates to a global conformal invariant as well as generalisations of the operators and the q curvature among examples the operators of order 4 6 and 8 and the related q curvatures are treated explicitly the algorithm exploits the ambient metric construction of fefferman and graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions this is partly based on 12 where the relationship of the normal standard tractor bundle to the ambient construction is described

iteration processes for nonlinear lipschitzian strongly accretive mappings in lp spaces abstract suppose x l p or l p 1 p 2 let t x x be a lipschitzian and strongly accretive map with constant k 0 1 and lipschitz constant l satisfying p p 1 l 2 p 2 p 1 1 k define s x x by sx tx x for arbitrary x 0 x the sequence x n n 1 is defined by x n 1 1 n x n n sy n y n 1 n x n n sx n n 0 where n n 1 n n 1 are two real sequences satisfying i 0 n 2 1 p 2 p 1 1 k k n l 2 n p 2 p l 2 1 w n w l 2 1 2 n p 2 p 1 1 k k n l 2 n p 1 2 l 2 1 w n w l 2 1 2 n 1 1 for each n ii 0 n min w w l 2 1 1 w 4 p 1 l 2 k p 1 2 l 2 w 1 for each n iii n n where w p 2 p 1 1 k p 2 p l 2 then x n 1 converges strongly to the unique solution of tx moreover if n 2 1 p 2 p 1 1 k k l 2 p 2 p l 2 1 w w l 2 1 2 p 2 p 1 1 k k l 2 p 1 2 l 2 1 w w l 2 1 2 1 1 and n for each n and some 0 min w w l 2 1 1 w 4 p 1 l 2 k p 1 2 l 2 w 1 then x n 1 q p n 2 x 1 q where q denotes the solution of tx and 1 4 1 p 2 p 1 1 k k l 2 p 2 p l 2 1 w w l 2 1 2 2 p 2 p 1 1 k k l 2 p 1 2 l 2 1 w w l 2 1 2 1 1 0 1 a related result details with the iterative approximation of lipschitz strongly pseudocontractive maps in x

iterative solution of nonlinear equations with strongly accretive operators abstract let e be a real banach space with a uniformly convex dual suppose t e e is a strongly accretive map with bounded range such that for each e the equation tx has a solution in e it is proved that each of the two well known fixed point iteration methods the mann and ishikawa iteration methods under suitable conditions converges strongly to a solution of the equation tx furthermore our method shows that such a solution is necessarily unique explicit error estimates are given our results resolve in the affirmative an open problem j math anal appl 151 no 2 1990 460 and generalize important known results

the p adic weighted hardy cesaro operator and an application to discrete hardy inequalities abstract this paper aims to investigate the boundedness of the p adic analog of the weighted hardy cesaro operator u s f z p f s t t d t on weighted lebesgue spaces and weighted bmo spaces in each case we obtain the corresponding operator norms u s in particular these results have a surprising relevance to discrete hardy inequalities on the real field we prove a reverse bmo hardy inequality and give a necessary condition on so that the commutator of u s is bounded on l r q p n with symbols in bmo q p n

ishikawa iteration process for nonlinear lipschitz strongly accretive mappings abstract let e lp p 2 and let t e e be a lipschitzian and strongly accretive mapping let s e e be defined by sx tx x it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process x0 e xn 1 1 n xn ns 1 n xn nsxn n 0 converges strongly to the unique solution of tx a related result deals with the iterative approximation of fixed points for lipschitz strongly pseudocontractive mappings in e a consequence of our result gives an affirmative answer to a problem posed by c e chidume j math anal appl 151 no 2 1990 453 461

convergence theorems for φ strongly accretive and φ hemicontractive operators suppose that x is an arbitrary real banach space and t x x is a continuous strongly accretive operator it is shown that the nonlinear equation tx f has a unique solution and under certain conditions both the mann and ishikawa iteration methods with errors introduced by y xu 1998 j math anal appl 224 91 101 converge strongly to the solution a related result deals with the approximation of fixed points of hemicontractive operators

hardy type theorems on fourier transforms revised abstract we obtain new conditions on periodic integrable functions so that their transformed fourier series belong to l p this improves the classical hardy and bellman results a counterpart for the fourier transforms is also established our main tool is a new extension of the hausdorff young paley inequality for fourier transforms

the structure of the reverse holder classes in this paper we study the structure of the class of functions rhs which satisfy the reverse holder inequality with exponent s i to do so we introduce a new operator the minimal operator which is analogous to the hardy littlewood maximal operator and a new class of functions rhcc which plays the same role for rhs that the class ax does for the ap classes

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

on chidume s open questions and approximate solutions of multivalued strongly accretive mapping equations in banach spaces abstract some new convergence theorems of the ishikawa iteration process for multi valued pseudo contractive mappings and multi valued accretive mappings are obtained which affirmatively answer the open questions put forth by 4

hardy space estimates of hausdorff operators on the heisenberg group abstract this is a continuation of a series of works about hausdorff operator on hardy spaces in the setting of the heisenberg group in this paper we obtain the boundedness from lebesgue spaces to hardy spaces for fractional hausdorff operators and their compositions with riesz transforms we also establish the boundedness for two kinds of special hausdorff operators the hausdorff poisson operator and the hausdorff gauss operator on hardy spaces

maximal operators riesz transforms and littlewood paley functions associated with bessel operators on bmo abstract in this paper we study boundedness properties of certain harmonic analysis operators maximal operators for heat and poisson semigroups riesz transforms and littlewood paley g functions associated with bessel operators on the space bmo o r that consists of the odd functions with bounded mean oscillation on r

steepest descent approximations for accretive operator equations a necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi accretive operators defined on a uniformly smooth banach space miramare trieste march 1993

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

iterative solution of nonlinear equations of the φ strongly accretive type abstract letq 1 and letebe a realq uniformly smooth banach space lett e ebe a lipschitz strongly accretive operator and suppose the equationtx f f e has a solution it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process formula converges strongly to the unique solution of the equationtx f a related result deals with the approximation of fixed points of hemicontractive operators a class of operators which is much more general than the important class of strongly pseudocontractive operators

conformally invariant differential operators on minkowski space and their curved analogues this article describes the construction of a natural family of conformally invariant differential operators on a four dimensional pseudo riemannian manifold included in this family are the usual massless field equations for arbitrary helicity but there are many more besides the article begins by classifying the invariant operators on flat space this is a fairly straightforward task in representation theory best solved through the theory of verma modules the method generates conformally invariant operators in the curved case by means of penrose s local twistor transport

ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations abstract the purpose of this paper is to revise the definitions of ishikawa and mann iterative processes with errors by using a new inequality to study the unique solution of the nonlinear strongly accretive operator equationtx fand the convergence problem of ishikawa and mann iterative sequences for strongly pseudo contractive mappings without the lipschitz condition the results presented in this paper improve and extend the corresponding results in 4 5 7 10 12 15 16 in the more general setting in particular the open problem mentioned by chidume in 5 has been given an affirmative answer

estimates of weighted hardy littlewood averages on the p adic vector space abstract in the p adic vector space q p n we characterize those non negative functions defined on z p w q p 0 w p 1 for which the weighted hardy littlewood average u f z p f t t d t is bounded on l r q p n 1 r and on bmo q p n also in each case we find the corresponding operator norm u