Revista Matemática Iberoamericana


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Volume 4, Issue 1, 1988, pp. 123–153
DOI: 10.4171/RMI/66

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

Patrick Ahern[1] and Joaquim Bruna[2]

(1) Department of Mathematics, University of Wisconsin at Madison, WI 53706, MADISON, UNITED STATES
(2) Departament de Matemàtiques, Universitat Autonoma de Barcelona, 08193, 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 P, Bruna J. 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