
- 416 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Multi-parameter Singular Integrals, Volume I
About this book
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. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. Multi-parameter Singular Integrals will interest graduate students and researchers working in singular integrals and related fields.
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Information
Table of contents
- Cover Page
- Title Page
- Copyright Page
- Contents
- Preface
- 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