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Calderón-Zygmund Capacities and Operators on Nonhomogeneous Spaces by Alexander Volberg is a book available to read on EtoBox.

What is Calderón-Zygmund Capacities and Operators on Nonhomogeneous Spaces about?

Singular integral operators play the central part in modern harmonic analysis. Simplest examples of singular kernels are given by Calderón–Zygmund kernels. Many important properties of singular integrals have been thoroughly studied for Calderón–Zygmund operators. In the'80s and early'90s, Coifman, Weiss, and Christ noticed that the theory of Calderón–Zygmund operators can be generalized from Euclidean spaces to spaces of homogeneous type. The purpose of this book is to make the reader believe that homogeneity (previously considered as a cornerstone of the theory) is not needed. This claim is illustrated by presenting two harmonic analysis problems famous for their difficulty. The first problem treats semiadditivity of analytic and Lipschitz harmonic capacities. The volume presents the first self-contained and unified proof of the semiadditivity of these capacities. The book details Tolsa's solution of Painlevé's and Vitushkin's problems and explains why these are problems of the theory of Calderón–Zygmund operators on nonhomogeneous spaces. The exposition is not dimension-specific, which allows the author to treat Lipschitz harmonic capacity and analytic capacity at the same time.

Author

Alexander Volberg

Publisher

American Mathematical Society for the Conference Board of the Mathematical Sciences

Published

2003

Language

EN

ISBN

9781470424619

Subjects

Mathematics, Stem