Sampling sequences for Hardy spaces of the ball
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- by Xavier Massaneda and Pascal J. Thomas PDF
- Proc. Amer. Math. Soc. 128 (2000), 837-843 Request permission
Abstract:
We show that a sequence $a:=\{a_{k}\}_{k}$ in the unit ball of $\mathbb {C}^{n}$ is sampling for the Hardy spaces $H^{p}$, $0<p<\infty$, if and only if the admissible accumulation set of $a$ in the unit sphere has full measure. For $p=\infty$ 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 $H^{\infty }$ whose admissible accumulation set has measure 0. We also consider the sequence $a(\omega )$ obtained by applying to each $a_{k}$ a random rotation, and give a necessary and sufficient condition on $\{|a_{k}|\}_{k}$ so that, with probability one, $a(\omega )$ is of sampling for $H^{p}$, $p<\infty$.References
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Additional Information
- Xavier Massaneda
- Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08071-Barcelona, Spain
- Email: xavier@cerber.mat.ub.es
- Pascal J. Thomas
- Affiliation: Laboratoire Emile Picard, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
- MR Author ID: 238303
- Email: pthomas@cict.fr
- Received by editor(s): May 4, 1998
- Published electronically: July 28, 1999
- Additional Notes: Both authors were partially supported by a program of the Comunitat de Treball dels Pirineus. The second author was also supported by DGICYT grant PB95-0956-C02-01 and CIRIT grant GRQ94-2014.
- Communicated by: Steven R. Bell
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 837-843
- MSC (1991): Primary 32A35, 32A30; Secondary 30B20, 30D50
- DOI: https://doi.org/10.1090/S0002-9939-99-05212-0
- MathSciNet review: 1646200