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

Author(s): D. A. Redett
Journal: Proc. Amer. Math. Soc. 133 (2005), 1151-1156.
MSC (2000): Primary 47A15; Secondary 46E30
Posted: October 15, 2004
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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:

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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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