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Hausdorff-Young inequalities for functions in Bergman spaces on tube domains

Published online by Cambridge University Press:  20 January 2009

David Bekollé  and
Aline Bonami
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Abstract

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We prove that the functions of the Bergman spaces Ap on tube domains may be written as Laplace transforms of functions when 1 ≤ p ≤ 2. We give in this context a generalization of the Hausdorff–Young inequality with the exact constant, and deduce from the case p = 2 the expression of the Bergman kernel as a Laplace transform.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 3 , October 1998 , pp. 553 - 566
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

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