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A note on interpolation in the Hardy spaces
of the unit disc

Authors: Joaquim Bruna, Artur Nicolau and Knut Øyma
Journal: Proc. Amer. Math. Soc. 124 (1996), 1197-1204
MSC (1991): Primary 30D55, 30D50; Secondary 46J15
MathSciNet review: 1307499
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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 [Enhancements On Off] (What's this?)

  • 1. U. Cegrell, A generalization of the corona theorem in the unit disc, Math. Z. 203 (1990). MR 91h:30059
  • 2. V. Kabaila, Interpolation sequences for the $H_p$ classes in the case $p<1$, Litovsk. Mat. Sb. 3 (1963), no. 1, 141--147. MR 32:217
  • 3. H. S. Shapiro and A. L. Shields, On some interpolation problems for analytic functions, Amer. J. Math. 83 (1961), 513--532. MR 24:A3280
  • 4. 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. MR 85c:30037

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Additional Information

Joaquim Bruna

Artur Nicolau
Affiliation: Department of Mathematics, University Autonoma de Bar- celona, 08193 Barcelona, Bellaterra, Spain

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
Article copyright: © Copyright 1996 American Mathematical Society