“Beurling type” subspaces of 𝐿^{𝑝}(𝐓²) and 𝐇^{𝐩}(𝐓²)

Redett, D.

doi:10.1090/S0002-9939-04-07616-6

“Beurling type” subspaces of $L^p(\mathbf {T}^2)$ and $H^p(\mathbf {T}^2)$
HTML articles powered by AMS MathViewer

by D. A. Redett PDF

Proc. Amer. Math. Soc. 133 (2005), 1151-1156 Request permission

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

Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
P. Ghatage and V. Mandrekar, On Beurling type invariant subspaces of $L^2(\textbf {T}^2)$ and their equivalence, J. Operator Theory 20 (1988), no. 1, 83–89. MR 972182
Henry Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. MR 0171178
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
Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841