Wavelets and Singular Integrals on Curves Surfaces

Wavelets are a recently developed tool for the analysis and synthesis of functions; The book was conceived for a graduate student, or researcher, with a primary interest in analysis (and preferably some knowledge of harmonic analysis and seeking an understanding of some of the new "real-variable methods" used in harmonic analysis. Wavelets are a recently developed tool for the analysis and synthesis of functions. This text begins with an introduction to the theory of wavelets and limits itself to the detailed construction of various orthonormal bases of wavelets. The second section of the book focuses on a criterion for the L2-boundedness of singular integral operators, known as the T(b) theorem. The book concludes with a survey of recent attempts to understand the geometry of subsets of Rn, in which analogues of the Cauchy kernel define bounded operators.