Note on vector valued Hardy spaces related to analytic functions having distributional boundary values

Abstract

Analytic functions defined on a tube domain $T^C\subset {\mathbb{C}}^n$ and taking values in a Banach space $X$ which are known to have $X$-valued distributional boundary values are shown to be in the Hardy space $H^p(T^C,X)$ if the boundary value is in the vector valued Lebesgue space $L^p({\mathbb{R}}^n,X)$, where $1\le p\le \infty$ and $C$ is a regular open convex cone. Poisson integral transform representations of elements of $H^p(T^C,X)$ are also obtained for certain classes of Banach spaces, including reflexive Banach spaces.

arXiv comment5 pages

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