Hardy-Sobolev spaces of complex tangential derivatives of holomorphic functions in domains of finite type

Abstract

In this paper, we prove Fefferman-Stein like characterizations of Hardy-Sobolev spaces of complex tangential derivatives of holomorphic functions in domains of finite type in $\boldsymbol C^n$. We also study the relationship between these complex tangential Hardy-Sobolev spaces and the usual ones. We also obtain partial results on domains not necessarily of finite type.