Multi-parameter Singular Integrals. (AM-189), Volume I / / Brian Street.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Street, Brian,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2014]; ©2015
• Year of Publication: 2014
• Edition: Course Book
• Language: English
• Series: Annals of Mathematics Studies ; 189
• Physical Description: 1 online resource (416 p.) :; 7 line illus.
• Other title: Frontmatter --; 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 --; Appendix A. Functional Analysis --; Appendix B. Three Results from Calculus --; Appendix C. Notation --; Bibliography --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400852758; 9783110494914; 9783110665925
• DOI: 10.1515/9781400852758
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Brian Street.

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.