Vector-Valued Analytic Functions Having Vector-Valued Tempered Distributions as Boundary Values

Abstract

Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1≤p2, if the boundary value is in the vector-valued Lp,1≤p2, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2≤p≤∞. Thus, with the addition of the results of this paper, the considered problems are proved for all p,1≤p≤∞.

Keywords

• Hardy space
• vector-valued analytic function
• distribution