Vector valued Hardy spaces related to analytic functions having distributional boundary values

Abstract

The Hardy space $H^p$ of vector valued analytic functions in tube domains in ${\mathbb{C}}^n$ and with values in Banach space are defined. Vector valued analytic functions in tube domains in ${\mathbb{C}}^n$ with values in Hilbert space and which have vector valued tempered distributions as boundary value are proved to be in $H^p$ corresponding to Hilbert space if the boundary value is in $L^p$ with values in Hilbert space. A Poisson integral representation for such vector valued analytic functions is obtained.

21 pages