In this paper we deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of , 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 itself involving only complex-tangential derivatives.
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Patrick Ahern, Joaquim Bruna, Maximal and Area Integral Characterizations of Hardy-Sobolev Spaces in the Unit Ball of . Rev. Mat. Iberoam. 4 (1988), no. 1, pp. 123–153DOI 10.4171/RMI/66