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Certain Invariant Subspaces of H2 and L2 on a Bidisc

Published online by Cambridge University Press:  20 November 2018

Takahiko Nakazi
Takahiko Nakazi*
Affiliation:
Hokkaido University, Sapporo, Japan
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We let T2 be the torus that is the cartesian product of 2 unit circles in C. The usual Lebesgue spaces, with respect to the Haar measure m of T2, are denoted by Lp = Lp(T2), and Hp = Hp(T2) is the space of all f in LP whose Fourier coefficients

are 0 as soon as at least one component of (j, ℓ) is negative.

A closed subspace M of L2 is said to be invariant if

Whenever this is the case, it follows that fM ⊂ M for every f in H∞. One can ask for a classification or an explicit description (in some sense) of all invariant subspaces of L2, but this seems out of reach.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 5 , 01 October 1988 , pp. 1272 - 1280
Copyright
Copyright © Canadian Mathematical Society 1988

References

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