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Two Multiplier Theorems for H1(U2)

Published online by Cambridge University Press:  20 January 2009

Daniel M. Oberlin
Daniel M. Oberlin
Affiliation:
Florida State University, Tallahassee, Florida 32306
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Let H1(U2) be the Hardy space of the bidisc as described in (3). Each function f ∈ H1(U2) has a Taylor expansion of the form . For 0<p<∞, a doubly-indexed sequence is said to be a multiplier of H1(U2) into lp if

This paper is concerned with the cases p = 2 and p = 1. Theorem 1 characterises the multipliers of into l2 and is an analogue in two variables of an old result of Hardy and Littlewood. Theorem 2 characterises the sequences (an)n≥0 such that (an+m)n,m≥0 is a multiplier of H1(U) into l1

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 1 , February 1979 , pp. 43 - 47
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

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