Darstellung skalarer und vektorwertiger Distributionen aus D?Lp durch Randwerte holomorpher Funktionen

Abstract

In the present paper we show that every distribution T in D′Lp (D′Lp(E) in the vector-valued case) has a representation as boundary value of a holomorphic function T (with values in E). This problem was considered in [1], [5], [12]. The representing functions are characterized by growth conditions. It is shown that the conditions in [1] and [5] don't extend to the vector-valued case while the conditions in [12] do.