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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on interpolation in the Hardy spaces of the unit disc
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by Joaquim Bruna, Artur Nicolau and Knut Øyma PDF
Proc. Amer. Math. Soc. 124 (1996), 1197-1204 Request permission

Abstract:

In this note we formulate and solve a natural interpolation problem for the Hardy spaces in the unit disc in terms of maximal functions and weighted summable sequences.
References
  • Urban Cegrell, A generalization of the corona theorem in the unit disc, Math. Z. 203 (1990), no. 2, 255–261. MR 1033435, DOI 10.1007/BF02570734
  • V. Kabaila, Interpolation sequences for the $H_{p}$ classes in the case $p<1$, Litovsk. Mat. Sb. 3 (1963), no. 1, 141–147 (Russian, with Lithuanian and English summaries). MR 0182735
  • H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513–532. MR 133446, DOI 10.2307/2372892
  • V. I. Vasyunin, Characterization of finite unions of Carleson sets in terms of solvability of interpolation problems, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 135 (1984), 31–35 (Russian, with English summary). Investigations on linear operators and the theory of functions, XIII. MR 741692
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Additional Information
  • Joaquim Bruna
  • Email: bruna@mat.uab.es
  • Artur Nicolau
  • Affiliation: Department of Mathematics, University Autonoma de Bar- celona, 08193 Barcelona, Bellaterra, Spain
  • Email: nicolau@mat.uab.es
  • Knut Øyma
  • Affiliation: Department of Mathematics, Agder College, P.O. Box 607, N-4601 Kristiansand, Norway
  • Received by editor(s): February 25, 1994
  • Received by editor(s) in revised form: October 13, 1994
  • Additional Notes: The first two authors were partially supported by DGICYT grant PB92-0804-C02-02, Spain
  • Communicated by: Albert Baernstein II
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 1197-1204
  • MSC (1991): Primary 30D55, 30D50; Secondary 46J15
  • DOI: https://doi.org/10.1090/S0002-9939-96-03168-1
  • MathSciNet review: 1307499