Brangesian spaces in 𝐻^{𝑝}(𝐓²)

Brangesian spaces in $H^p(\mathbf {T}^2)$
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by D. A. Redett

Proc. Amer. Math. Soc. 133 (2005), 2689-2695

DOI: https://doi.org/10.1090/S0002-9939-05-07833-0

Published electronically: March 22, 2005

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In this note, we characterize certain algebraic subspaces of $H^p(\mathbf {T}^2)$ extending D. Singh’s $H^2(\mathbf {T}^2)$ result.

References

V. Mandrekar, The validity of Beurling theorems in polydiscs, Proc. Amer. Math. Soc. 103 (1988), no. 1, 145–148. MR 938659, DOI 10.1090/S0002-9939-1988-0938659-7
D. A. Redett, “Beurling Type” Subspaces of $L^p(\mathbf {T}^2)$ and $H^p(\mathbf {T}^2)$, Proc. Amer. Math. Soc., 133 no. 4 (2005), 1151–1156.
Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
Dinesh Singh, Brangesian spaces in the polydisk, Proc. Amer. Math. Soc. 110 (1990), no. 4, 971–977. MR 1028289, DOI 10.1090/S0002-9939-1990-1028289-2
Dinesh Singh and Sanjeev Agrawal, de Branges spaces contained in some Banach spaces of analytic functions, Illinois J. Math. 39 (1995), no. 3, 351–357. MR 1339831
Marek Słociński, On the Wold-type decomposition of a pair of commuting isometries, Ann. Polon. Math. 37 (1980), no. 3, 255–262. MR 587496, DOI 10.4064/ap-37-3-255-262
Alberto Torchinsky, Real-variable methods in harmonic analysis, Pure and Applied Mathematics, vol. 123, Academic Press, Inc., Orlando, FL, 1986. MR 869816