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Multipliers of Bergman spaces into Lebesgue spaces

Published online by Cambridge University Press:  20 January 2009

Daniel H. Luecking
Daniel H. Luecking
Affiliation:
University of Arkansas, Fayetteville, Arkansas 72701
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Let U be the open unit disk in the complex plane endowed with normalized Lebesgue measure m. will denote the usual Lebesgue space with respect to m, with 0<p<+∞. The Bergman space consisting of the analytic functions in will be denoted . Let μ be some positivefinite Borel measure on U. It has been known for some time (see [6] and [9]) what conditions on μ are equivalent to the estimate: There is a constant C such that

provided 0<p≦q.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 1 , February 1986 , pp. 125 - 131
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

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