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.