Multi-Parameter Singular Integrals. (Am-189), Volume I

The book presents a groundbreaking theory of multi-parameter singular integrals linked to Carnot-Carathéodory balls, beginning with a comprehensive overview of Calderón-Zygmund singular integrals and their relevance to linear partial differential equations. It explores multi-parameter Carnot-Carathéodory geometry, utilizing a quantitative version of Frobenius's theorem. Through various examples, it illustrates the natural emergence of these integrals in different contexts. The concluding chapter establishes a unifying general theory, appealing to graduate students and researchers in singular integrals and related disciplines.