TY - BOOK AU - Street,Brian TI - Multi-parameter singular integrals T2 - Annals of mathematics sudies SN - 9780691162522 (pbk. : alk. paper) U1 - 515.98 23 PY - 2014/// CY - Princeton : PB - Princeton University Press, KW - Singular integrals KW - Transformations (Mathematics) N1 - 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 N2 - 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 ER -