Street Multi-parameter Singular Integrals, Volume I

Course Book
ISBN: 978-1-4008-5275-8
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 416 Seiten

Reihe: Annals of Mathematics Studies

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.

Autoren/Hrsg.

Street, Brian

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

FrontMatter, pg. i
Contents, pg. v
Preface, pg. ix
1. The Calderón-Zygmund Theory I: Ellipticity, pg. 1
2. The Calderón-Zygmund Theory II: Maximal Hypoellipticity, pg. 39
3. Multi-parameter Carnot-Carathéodory Geometry, pg. 198
4. Multi-parameter Singular Integrals I: Examples, pg. 223
5. Multi-parameter Singular Integrals II: General Theory, pg. 268
Appendix A. Functional Analysis, pg. 363
Appendix B. Three Results from Calculus, pg. 376
Appendix C. Notation, pg. 380
Bibliography, pg. 383
Index, pg. 393

Über Autor(innen)

Brian Street is assistant professor of mathematics at the University of Wisconsin–Madison.