Maximal Function Methods for Sobolev Spaces

Maximal Function Methods for Sobolev Spaces
ISBN-10
1470465752
ISBN-13
9781470465759
Category
Education
Pages
354
Language
English
Published
2021-08-02
Publisher
American Mathematical Soc.
Authors
Juha Kinnunen, Juha Lehrbäck, Antti Vähäkangas

Description

This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.

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