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Title: Sampling sequences for Hardy spaces of the ball
Author: Massaneda Clares, Francesc Xavier
Thomas, Pascal J.
Keywords: Funcions holomorfes
Espais de Hardy
Holomorphic functions
Series expansions
Issue Date: 2000
Publisher: American Mathematical Society
Abstract: We show that a sequence a:= {ak}k in the unit ball of Cn is sampling for the Hardy spaces Hp, 0 < p < ∞ , if and only if the admissible accumulation set of a in the unit sphere has full measure. For p = ∞ the situation is quite different. While this condition is still sufficient, when n > 1 (in contrast to the one dimensional situation) there exist sampling sequences for H∞ whose admissible accumulation set has measure 0. We also consider the sequence a(ω ) obtained by applying to each ak a random rotation, and give a necessary and sufficient condition on {|ak|}k so that, with probability one, a(ω ) is of sampling for Hp, p < ∞ .
Note: Reproducció digital del document publicat en format paper, proporcionada per JSTOR
It is part of: Proceedings of the American Mathematical Society, 2000, vol. 128, núm. 3, p. 837-843.
ISSN: 1088-6826
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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