Multi-parameter Singular Integrals. (AM-189), Volume I [Paperback]

This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carath?odory balls. Brian Street first details the classical theory of Calder?n-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Carath?odory 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 Integralswill interest graduate students and researchers working in singular integrals and related fields.