Morrey Spaces

by Yoshihiro Sawano

Author	: Yoshihiro Sawano
Publisher	: CRC Press
Total Pages	: 316
Release	: 2020-09-16
Genre	: Mathematics
ISBN	: 1000064077

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Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Morrey Spaces

by David Adams

Author	: David Adams
Publisher	: Birkhäuser
Total Pages	: 133
Release	: 2015-12-31
Genre	: Mathematics
ISBN	: 3319266810

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In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any “full” interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory.

Morrey Spaces

by Yoshihiro Sawano

Author	: Yoshihiro Sawano
Publisher	: CRC Press
Total Pages	: 503
Release	: 2020-09-16
Genre	: Mathematics
ISBN	: 1498765521

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Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume I focused mainly on harmonic analysis. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Weighted Morrey Spaces

by Marcus Laurel

Author	: Marcus Laurel
Publisher	: Walter de Gruyter GmbH & Co KG
Total Pages	: 367
Release	: 2024-09-02
Genre	: Mathematics
ISBN	: 3111461459

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This monograph is a testament to the potency of the method of singular integrals of layer potential type in solving boundary value problems for weakly elliptic systems in the setting of Muckenhoupt-weighted Morrey spaces and their pre-duals. A functional analytic framework for Muckenhoupt-weighted Morrey spaces in the rough setting of Ahlfors regular sets is built from the ground up and subsequently supports a Calderón-Zygmund theory on this brand of Morrey space in the optimal geometric environment of uniformly rectifiable sets. A thorough duality theory for such Morrey spaces is also developed and ushers in a never-before-seen Calderón-Zygmund theory for Muckenhoupt-weighted Block spaces. Both weighted Morrey and Block spaces are also considered through the lens of (generalized) Banach function spaces, and ultimately, a variety of boundary value problems are formulated and solved with boundary data arbitrarily prescribed from either scale of space. The fairly self-contained nature of this monograph ensures that graduate students, researchers, and professionals in a variety of fields, e.g., function space theory, harmonic analysis, and PDE, will find this monograph a welcome and valuable addition to the mathematical literature.

Morrey and Campanato Meet Besov, Lizorkin and Triebel

by Wen Yuan

Author	: Wen Yuan
Publisher	: Springer Science & Business Media
Total Pages	: 295
Release	: 2010-09-18
Genre	: Mathematics
ISBN	: 3642146058

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During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞.

Harmonic Analysis

by Satoru Igari

Author	: Satoru Igari
Publisher	:
Total Pages	: 228
Release	: 1991
Genre	: Electronic books
ISBN	:

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Contents: G. Alexopoulos: Parabolic Harnack inequalities and Riesz transforms on Lie groups of polynomial growth.- H. Arai: Harmonic analysis with respect to degenerate Laplacian on strictly pseudoconvex domains.- J.M. Ash, R. Brown: Uniqueness and nonuniqueness for harmonic functions with zero nontangential limits.- A. Carbery, E. Hernndez, F. Soria: Estimates for the Kakeya maximal operator on radial functions in Rn.- S.-Y.A. Chang, P.C. Yang: Spectral invariants of conformal metrics.- M. Christ: Remarks on the breakdown of analycity for b and Szeg kernels.- R. Coifman, S. Semmes: L2 estimates in nonlinear Fourier analysis.- Dinh Dung: On optimal recovery of multivariate periodic functions.- S.A.A. Emara: A class of weighted inequalities.- G.I. Gaudry: Some singular integrals on the affine group.- J.-P. Kahane: From Riesz products to random sets.- T. Kawazoe: A model of reduction in harmonic analysis on real rank 1 semisimple Lie groups I.- P.G. Lemari: Wavelets, spline interpolation and Lie groups.- P. Mattila: Principle values of Cauchy integrals, rectifiable measures and sets.- A. Miyachi: Extension theorems for real variable Hardy and Hardy-Sobolev spaces.- T. Mizuhara: Boundedness of some classical operators on generalized Morrey spaces.- G. Sinnamon: Interpolation of spaces defined by the level function.- T.N. Varopoulos: Groups of superpolynomial growth.- J.M. Wilson: Littlewood-Paley theory in one and two parameters.- J.M. Wilson: Two-weight norm inequalities for the Fourier transform.- Program.- List of participants.

The Navier-Stokes Equations

by Hermann Sohr

Author	: Hermann Sohr
Publisher	: Springer Science & Business Media
Total Pages	: 376
Release	: 2012-12-13
Genre	: Mathematics
ISBN	: 3034805519

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The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.

Topics in Contemporary Mathematical Analysis and Applications

by Hemen Dutta

Author	: Hemen Dutta
Publisher	: CRC Press
Total Pages	: 339
Release	: 2020-12-22
Genre	: Mathematics
ISBN	: 1000204219

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Topics in Contemporary Mathematical Analysis and Applications encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. The readers will find developments concerning the topics presented to a reasonable extent with various new problems for further study. Each chapter carefully presents the related problems and issues, methods of solutions, and their possible applications or relevancies in other scientific areas. Aims at enriching the understanding of methods, problems, and applications Offers an understanding of research problems by presenting the necessary developments in reasonable details Discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems This book is written for individual researchers, educators, students, and department libraries.

Operator Theory, Pseudo-Differential Equations, and Mathematical Physics

by Yuri I. Karlovich

Author	: Yuri I. Karlovich
Publisher	: Springer Science & Business Media
Total Pages	: 425
Release	: 2012-10-30
Genre	: Mathematics
ISBN	: 3034805373

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This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) includes a short biography of Vladimir Rabinovich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich's research interests. Many of them are written by participants of the International workshop “Analysis, Operator Theory, and Mathematical Physics” (Ixtapa, Mexico, January 23–27, 2012) having a long history of scientific collaboration with Vladimir Rabinovich, and are partially based on the talks presented there.The volume will be of great interest to researchers and graduate students in differential equations, operator theory, functional and harmonic analysis, and mathematical physics.