Displaying similar documents to “On L p -solutions of the Laplace equation and zeros of holomorphic functions”

Subsets of Hardy-class zero sets in the ball.

Pascal J. Thomas (1990)

Publicacions Matemàtiques

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We consider the problem of whether the union of complex hyperplanes can be a subset of a zero variety for the Hardy classes of the ball. A sufficient condition is found, consisting in a strong geometric separatedness requirement, together with a quantitative requirement slightly stronger than the necessary condition for Nevanlinna class zero varieties.

Maximal and area integral characterizations of Hardy-Soboley spaces in the unit ball of C.

Patrick Ahern, Joaquim Bruna (1988)

Revista Matemática Iberoamericana

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In this paper we deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of C, that is, spaces of holomorphic 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 itself involving only complex-tangential...