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Function Spaces and Partial Differential Equations
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Function Spaces and Partial Differential Equations: Volume 1 - Classical Analysis

Ali Taheri

Abstract

This book, which is the first volume of two, presents a comprehensive treatment of aspects of classical and modern analysis relating to theory of ‘partial differential equations’ and the associated ‘function spaces’. It begins with a quick review of basic properties of harmonic functions and Poisson integrals and then moves into a detailed study of Hardy spaces. The classical Dirichlet problem is considered and a variety of methods for its resolution ranging from potential theoretic (Perron’s method of sub-harmonic functions and Wiener’s criterion, Green’s functions and Poisson integrals, the ... More

Keywords: partial differential equations, harmonic analysis, function spaces, regularity theory, harmonic functions, Laplace operator, Sobolev spaces, BMO, Hardy spaces, Besov spaces, Triebel-Lizorkin spaces

Bibliographic Information

Print publication date: 2015 Print ISBN-13: 9780198733133
Published to Oxford Scholarship Online: September 2015 DOI:10.1093/acprof:oso/9780198733133.001.0001

Authors

Affiliations are at time of print publication.

Ali Taheri, author
Reader in Mathematics, University of Sussex