Mar 04, 2011 morrey spaces in harmonic analysis morrey spaces in harmonic analysis adams, david. A nonexistence result on harmonic diffeomorphisms between punctured spaces du, shizhong and fan, xuqian, differential and integral equations, 2016. Preduals of morrey spaces have been studied by many authors, see the recent book 1 and the paper 12 for further details and references. When the underlying spaces are the nonhomogeneous spaces of hyt.
The point here is that the subject of harmonic analysis is a point of view and a collection of tools, and harmonic analysts continually seek new venues in which to ply their wares. Besov morrey spaces associated with the hermite operators. This material is the framework from which to attack harmonic analysis on more general spaces. Crossref javier duoandikoetxea and marcel rosenthal, extension and boundedness of operators on morrey spaces from extrapolation techniques and embeddings, the journal of geometric analysis, 10. Morrey spaces in harmonic analysis 203 here and henceforth, for 0 morrey spaces and fine regularity of solutions to pdes article pdf available in potential analysis 203. New function spaces related to morrey spaces and the fourier transform nakamura, shohei and sawano, yoshihiro, banach journal of mathematical analysis, 2018. Request pdf morrey spaces in harmonic analysis through a geometric capacitary analysis based on space dualities, this paper addresses several. Morrey spaces were introduced recently and studied by several. Morrey spaces for nonhomogeneous metric measure spaces. Morrey spaces in harmonic analysis morrey spaces in harmonic analysis adams, david. Preduals of morrey spaces have been studied by many authors, see the recent book 1 and the paper 14 for further details and references.
After this material one can begin chapter 6 on representation theory. In recent years, there is an explosion of interest in morrey type spaces and their applications, see 34, 46 and references therein. The wavefront sets and products of distributions 345 4. For example, local morrey spaces play important role to describe the real interpolation of weighted lebesgue spaces, which covers the o. Advances in harmonic analysis and operator theory the. Through a geometric capacitary analysis based on space dualities, this paper addresses several fundamental aspects of functional analysis and potential theory for the morrey spaces in harmonic analysis over the euclidean spaces.
Boundedness of some sublinear operators on weighted. The chapter gives important examples coming from classical matrix groups and their homogeneous spaces. Polysuperharmonic functions on a harmonic space alqurashi, m. The geometric cauchy problem for surfaces with lorentzian harmonic gauss maps brander, david and svensson, martin, journal of differential. In this set of lecture notes, the author includes some of the latest research on the theory of morrey spaces associated with harmonic analysis. This new family of spaces was introduced by morrey and charles in for the study of partial differential equations. There are three main claims concerning these spaces that are covered.
Morrey spaces and fractional operators journal of the. Since then, morrey type spaces have achieved a rapid development. View enhanced pdf access article on wiley online library html view download pdf for offline. A description of all the admissible weights similar to the muckenhoupt class a p is an open problem for the weighted morrey spaces. Pdf singular integral operators, morrey spaces and fine. Morrey in 1938 see 26 in order to study regularity questions which appear in the calculus of variations, describe local regularity more precisely than lebesgue spaces and widely use not only harmonic analysis but also partial di. Stein and his school introduced the idea of studying classical harmonic analysisfractional. In particular, the conference will encourage international collaboration and interactive activities on the modern problems on harmonic analysis and provide an opportunity for moroccans young researchers to learn the current state of the researches in this field of mathematics. A handbook of harmonic analysis yoshihiro sawano contents preface 10 acknowledgement 10 orientation of this book 10 notations in this book part 1. This closure plays an important role in harmonic analysis on morrey spaces, including calderonzygmund theory, since its dual constitutes a predual of morrey spaces cf. Sawano, yoshihiro sugano, satoko and tanaka, hitoshi 2012.
Morrey spaces lecture notes in applied and numerical harmonic analysis kindle edition by david adams. Holder spaces, sobolev spaces and bmo functions polam yung the chinese university of hong kong. Available formats pdf please select a format to send. Sobolev and morrey embedding theorems i the sobolev embedding theorem describes continuous embeddings of sobolev spaces into appropriate lq. In 26, mizuhara studied a version of generalized morrey spaces and got the boundedness of caldero. Research article morrey spaces for nonhomogeneous metric. In addition, the related theories for morrey spaces promise developments of this field in the near future. In this paper, we shall introduce a weighted morrey space and study the several properties of classical operatorsin harmonic analysis on this space 2009 wiley. Sep 26, 2018 weighted morreytype classes of functions that are harmonic in the unit disk and in the upper half plane are defined in this work. Singular integral operators, morrey spaces and fine regularity of solutions to pdes article pdf available in potential analysis 203. Weighted morrey spaces and a singular integral operator. Calculus of variations, describe local regularity more precisely than lebesgue spaces and widely use not only harmonic analysis but also partial differential.
Hp spaces and boundary values of analytic functions on the unit. Last two decades there is an increasing interest to the study of variable ex. Morrey spaces lecture notes in applied and numerical. Xu, boundedness of rough singular intergral operators on the homogeneous morrey herz spaces, hokkaido math. Estimation of the maximum values of harmonic functions for a nontangential angle through the hardylittlewood maximal function are generalized to more. Morrey spaces in harmonic analysis, arkiv for matematik.
Let wa be the set of continuous increasing concave functions 0,a r. Morrey spaces in harmonic analysis request pdf researchgate. It is a useful reference to mathematicians working in potential theory, harmonic analysis and partial differential equations. Morrey spaces applied and numerical harmonic analysis. Use features like bookmarks, note taking and highlighting while reading morrey spaces lecture notes in applied and numerical harmonic analysis.
We believe that our contribution will be of strong interest either for the theory of function spaces itself or from the applications point of view. Morrey spaces were introduced by charles morrey to investigate the local behaviour of solutions to second order elliptic partial di. The contributions display the range of his scientific interests in harmonic analysis and operator theory. In this paper, the authors prove the boundedness of the multilinear maximal functions, multilinear singular integrals and multilinear riesz potential on the product generalized morrey spaces mp1. Morrey spaces in harmonic analysis 203 here and henceforth, for 0 spaces related to morrey spaces and the fourier transform nakamura, shohei and sawano, yoshihiro, banach journal of mathematical analysis, 2018.
Interpolation of morrey spaces on metric measure spaces. In this paper we study the boundedness for a large class of sublinear operators t generated by calderonzygmund operators on generalized weighted morrey spaces m p. Morrey spaces in harmonic analysis, arkiv for matematik 10. Hardy spaces hp for 0 in hardy h p spaces on tubes for 1 p 1are given, for f2l p r n.
Hu, herz type spaces and their applications, science press, beijing, 2008. Under some conditions on the weight function, we study some properties of functions belonging to these classes. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as. Different approaches and growth envelopes the journal of geometric analysis, apr 2017 dorothee d. Recently, moreandmorebanach lattices come intoplay inharmonic analysis. Holder spaces, sobolev spaces and bmo functions polam yung. Harmonic analysis obstacle problem morrey space atomic decomposition dyadic cube. Morrey spaces books pics download new books and magazines. Download it once and read it on your kindle device, pc, phones or tablets. Twoweight norm inequalities on morrey spaces hitoshi tanaka the university of tokyo, graduate school of mathematical sciences tokyo, 1538914, japan. The authors give a definition of morrey spaces for nonhomogeneous metric measure spaces and investigate the boundedness of some classical operators including maximal operator, fractional integral operator, and marcinkiewicz integral operators. Some questions of harmonic analysis in weighted morrey type. Boundedness of multilinear operators on generalized morrey.