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``Beurling type'' subspaces of $L^p(\mathbf{T}^2)$ and $H^p(\mathbf{T}^2)$


Author: D. A. Redett
Journal: Proc. Amer. Math. Soc. 133 (2005), 1151-1156
MSC (2000): Primary 47A15; Secondary 46E30
DOI: https://doi.org/10.1090/S0002-9939-04-07616-6
Published electronically: October 15, 2004
MathSciNet review: 2117217
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Abstract: In this note we extend the ``Beurling type'' characterizations of subspaces of $L^2(\mathbf{T}^2)$ and $H^2(\mathbf{T}^2)$ to $L^p(\mathbf{T}^2)$ and $H^p(\mathbf{T}^2)$, respectively.


References [Enhancements On Off] (What's this?)

  • 1. A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math., 81 (1949), 239-255. MR 10:381e
  • 2. P. Ghatage and V. Mandrekar, On Beurling type invariant subspaces of $L^2(\mathbf{T}^2)$ and their equivalence, J. Operator Theory, 20 (1988), 83-89. MR 90i:47005
  • 3. H. Helson, Lectures on invariant subspaces, Academic Press, 1964. MR 30:1409
  • 4. V. Mandrekar, The validity of Beurling theorems in polydiscs, Proc. Amer. Math. Soc., 103 (1988), 145-148. MR 90c:32008
  • 5. W. Rudin, Fourier Analysis on Groups, Interscience, 1962. MR 27:2808
  • 6. W. Rudin, Function theory in polydiscs, Benjamin, New York, 1969. MR 41:501

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Additional Information

D. A. Redett
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: redett@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07616-6
Received by editor(s): October 8, 2003
Received by editor(s) in revised form: December 2, 2003
Published electronically: October 15, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society

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