Morrey Spaces

Morrey Spaces
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

Morrey Spaces
Author: Yoshihiro Sawano
Publisher: CRC Press
Total Pages: 386
Release: 2020-09-17
Genre: Mathematics
ISBN: 0429532024
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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

Morrey Spaces

Morrey Spaces
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

Morrey Spaces
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

Weighted Morrey Spaces
Author: Marcus Laurel
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 432
Release: 2024-09-02
Genre: Mathematics
ISBN: 311145827X
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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

Morrey and Campanato Meet Besov, Lizorkin and Triebel
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 = ∞.

Function Spaces and Inequalities

Function Spaces and Inequalities
Author: Pankaj Jain
Publisher: Springer
Total Pages: 334
Release: 2017-10-20
Genre: Mathematics
ISBN: 981106119X
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This book features original research and survey articles on the topics of function spaces and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces, Lorentz spaces, and Morrey spaces and deals with mapping properties of operators, (weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers Sobolev–Besov and Triebel–Lizorkin type smoothness spaces. The book includes papers by leading international researchers, presented at the International Conference on Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on 11–15 December 2015, which focused on recent developments in the theory of spaces with variable exponents. It also offers further investigations concerning Sobolev-type embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a specific topic and written by leading experts, providing an overview of the subject and stimulating future research.

Harmonic Analysis

Harmonic Analysis
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.

Morrey Spaces

Morrey Spaces
Author: Yoshihiro Sawano
Publisher: CRC Press
Total Pages: 386
Release: 2020-06-08
Genre: Mathematics
ISBN: 1000064131
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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 focus on harmonic analysis in volume I and generalizations and interpolation of Morrey spaces in volume II. 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

MSCEIS 2019

MSCEIS 2019
Author: Lala Septem Riza
Publisher: European Alliance for Innovation
Total Pages: 1652
Release: 2020-07-30
Genre: Science
ISBN: 1631902563
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The 7th Mathematics, Science, and Computer Science Education International Seminar (MSCEIS) was held by the Faculty of Mathematics and Natural Science Education, Universitas Pendidikan Indonesia (UPI) and the collaboration with 12 University associated in Asosiasi MIPA LPTK Indonesia (AMLI) consisting of Universitas Negeri Semarang (UNNES), Universitas Pendidikan Indonesia (UPI), Universitas Negeri Yogyakarta (UNY), Universitas Negeri Malang (UM), Universitas Negeri Jakarta (UNJ), Universitas Negeri Medan (UNIMED), Universitas Negeri Padang (UNP), Universitas Negeri Manado (UNIMA), Universitas Negeri Makassar (UNM), Universitas Pendidikan Ganesha (UNDHIKSA), Universitas Negeri Gorontalo (UNG), and Universitas Negeri Surabaya (UNESA). In this year, MSCEIS 2019 takes the following theme: "Mathematics, Science, and Computer Science Education for Addressing Challenges and Implementations of Revolution-Industry 4.0" held on October 12, 2019 in Bandung, West Java, Indonesia.