Maximal and Area Integral Characterizations of Hardy-Sobolev Spaces in the Unit Ball of ${\mathbb{C}}^n$

Abstract

In this paper we deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of ${\mathbb{C}}^n$, that is, spaces of holomorphie functions in the ball whose derivatives up to a certain order belong to the classical Hardy spaces. Some of our characterizations are in terms of maximal functions, area functions or Littlewood-Paley functions involving only complex-tangential derivatives. A special case of our results is a characterization of $H^p$ itself involving only complex-tangential derivatives.