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European Mathematical Society Publishing House
2016-09-19 17:05:42
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
4
1988
1
Maximal and Area Integral Characterizations of Hardy-Sobolev Spaces in the Unit Ball of $\mathbb C^n$
Patrick
Ahern
University of Wisconsin at Madison, MADISON, UNITED STATES
Joaquim
Bruna
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.
General
123
153
10.4171/RMI/66
http://www.ems-ph.org/doi/10.4171/RMI/66