Decomposition of L ^p(∂D _a) space and boundary value of holomorphic functions

Abstract

This paper deals with two topics mentioned in the title. First, it is proved that function f in L ^p(∂D _a) can be decomposed into a sum g + h, where D _a is an angular domain in the complex plane, g and h are the non-tangential limits of functions in H ^p(D _a) and ${H^p}\left( {\overline D _a^c} \right)$ in the sense of L ^p(D _a), respectively. Second, the sufficient and necessary conditions between boundary values of holomorphic functions and distributions in n-dimensional complex space are obtained.

Keywords

Hardy space / Rational function / Holomorphic function / Distribution

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