Hausdorff-Young inequalities for functions in Bergman spaces on tube domains
- 1 October 1998
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 41 (3) , 553-566
Abstract
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.Keywords
This publication has 6 references indexed in Scilit:
- Reproducing properties and $L^p$-estimates for Bergman projections in Siegel domains of type IIStudia Mathematica, 1995
- Paley-Wiener type theorems for functions in Bergman spaces over tube domainsJournal of Mathematical Analysis and Applications, 1986
- Closed ranged restriction operators on weighted Bergman spacesPacific Journal of Mathematics, 1984
- Theory of Function Spaces1983
- Inequalities in Fourier AnalysisAnnals of Mathematics, 1975
- The Bergman kernel function for tubes over convex conesPacific Journal of Mathematics, 1962