Sampling sets for Hardy spaces of the disk
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- by Pascal J. Thomas PDF
- Proc. Amer. Math. Soc. 126 (1998), 2927-2932 Request permission
Abstract:
We propose two possible definitions for the notion of a sampling sequence (or set) for Hardy spaces of the disk. The first one is inspired by recent work of Bruna, Nicolau, and Øyma about interpolating sequences in the same spaces, and it yields sampling sets which do not depend on the value of $p$ and correspond to the result proved for bounded functions ($p=\infty$) by Brown, Shields and Zeller. The second notion, while formally closer to the one used for weighted Bergman spaces, leads to trivial situations only, but raises a possibly interesting problem.References
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Additional Information
- 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): October 14, 1996
- Received by editor(s) in revised form: February 27, 1997
- Communicated by: Theodore W. Gamelin
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2927-2932
- MSC (1991): Primary 30E10, 30D55, 30C15
- DOI: https://doi.org/10.1090/S0002-9939-98-04411-6
- MathSciNet review: 1452830