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Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces (Cbms Regional Conference Series in Mathematics) by Alexander Volberg is a nonfiction available to read on EtoBox.

What is Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces (Cbms Regional Conference Series in Mathematics) about?

Singular integral operators play a central role in modern harmonic analysis. Simplest examples of singular kernels are given by Calderon-Zygmund kernels. Many important properties of singular integrals have been thoroughly studied for Calderon-Zygmund operators. In the 1980's and early 1990's, Coifman, Weiss, and Christ noticed that the theory of Calderon-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 Painleve's and Vitushkin's problems and explains why these are problems of the theory of Calderon-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 t

Who reads Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces (Cbms Regional Conference Series in Mathematics)?

Author

Alexander Volberg

Publisher

American Mathematical Society for the Conference Board of the Mathematical Sciences

Published

2003

Language

EN

ISBN

9781470424619

Category

nonfiction

Subjects

Mathematics, Stem