JournalsrmiVol. 4, No. 1pp. 123–153

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

  • Patrick Ahern

    University of Wisconsin at Madison, USA
  • Joaquim Bruna

    Universitat Autonoma de Barcelona, Bellaterra, Spain
Maximal and Area Integral Characterizations of Hardy-Sobolev Spaces in the Unit Ball of $\mathbb C^n$ cover
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Abstract

In this paper we deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of Cn\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 HpH^p itself involving only complex-tangential derivatives.

Cite this article

Patrick Ahern, Joaquim Bruna, Maximal and Area Integral Characterizations of Hardy-Sobolev Spaces in the Unit Ball of Cn\mathbb C^n. Rev. Mat. Iberoam. 4 (1988), no. 1, pp. 123–153

DOI 10.4171/RMI/66