Revista Matemática Iberoamericana
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Maximal and Area Integral Characterizations of Hardy-Sobolev Spaces in the Unit Ball of $\mathbb C^n$Patrick Ahern and Joaquim Bruna (1) University of Wisconsin at Madison, USA
(2) Universitat Autonoma de Barcelona, Bellaterra, Spain
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.
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Ahern Patrick, Bruna Joaquim: Maximal and Area Integral Characterizations of Hardy-Sobolev Spaces in the Unit Ball of $\mathbb C^n$. Rev. Mat. Iberoamericana 4 (1988), 123-153. doi: 10.4171/RMI/66