Boundary behavior of Hardy spaces on angular domains

Abstract

The aim of this paper is to characterize the behavior of boundary limits of functions in Hardy space on angular domains. We investigate that the Cauchy integral of a function $$f\in L^{p}(\partial D_a)$$ is in $$H^{p}(D_a).$$ We also prove that the functions in $$H^{p}(D_a)$$ are the Cauchy integral of their non-tangential boundary limits. In addition, we establish the orthogonality of non-tangential boundary limits of functions in $$H^{p}(D_a)$$ and $$H^{q}(D_a)$$.