Multi-parameter Singular Integrals. (AM-189) (Annals of Mathematics Studies)

Synopsis

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.-- 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. Brian Street. Includes Bibliographical References And Index.