Harmonic Analysis Techniques in Several Complex Variables

Abstract

We give a survey of recent joint work with E.M. Stein (Princeton University) concerning the application of suitable versions of the T(1)-theorem technique to the study of orthogonal projections onto the Hardy and Bergman spaces of holomorphic functions for domains with minimal boundary regularity.

Keywords

• Cauchy Integral
• T(1)-theorem
• space of homogeneous type
• Leray-Levi measure
• Szegő projection
• Bergman projection
• Hardy space
• Bergman space
• Lebesgue space
• pseudoconvex domain
• minimal smoothness