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Multi-parameter singular integrals / Brian Street.

By: Material type: TextTextSeries: Annals of mathematics sudies ; no 189.Publication details: Princeton : Princeton University Press, c2014.Description: xiii, 395 p. ; 24 cmISBN:
  • 9780691162522 (pbk. : alk. paper)
Subject(s): DDC classification:
  • 515.98 23 St915
Contents:
1. The Calderón-Zygmund theory I : ellipticity -- 2. The Calderón-Zygmund theory II : maximal hypoellipticity -- 3. Multi-parameter Carnot-Carathéodory geometry -- 4. Multi-parameter singular integrals I : examples -- 5. Multi-parameter singular integrals II : general theory -- A. Functional analysis -- B. Three results from calculus -- C. Notation-- Bibliography-- Index.
Summary: This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carathéodory balls. Brian Street first details the classical theory of Calderón-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. Street then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples.
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Includes bibliographical references (pages 383-392) and index.

1. The Calderón-Zygmund theory I : ellipticity --
2. The Calderón-Zygmund theory II : maximal hypoellipticity --
3. Multi-parameter Carnot-Carathéodory geometry --
4. Multi-parameter singular integrals I : examples --
5. Multi-parameter singular integrals II : general theory --
A. Functional analysis --
B. Three results from calculus --
C. Notation--
Bibliography--
Index.

This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carathéodory balls. Brian Street first details the classical theory of Calderón-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. Street then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples.

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