Contractive inequalities for Bergman spaces and multiplicative Hankel forms

Bayart, F., Brevig, O. F., Haimi, A., Ortega-Cerdà, J. and Perfekt, K.-M. (2019) Contractive inequalities for Bergman spaces and multiplicative Hankel forms. Transactions of the American Mathematical Society, 371 (1). pp. 681-707. ISSN 1088-6850 doi: 10.1090/tran/7290

Abstract/Summary

We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimetric inequality and of Weissler's inequality for dilations. By contractivity and a standard tensorization procedure, the unit disc inequalities yield corresponding inequalities for the Bergman spaces of Dirichlet series. We use these results to study weighted multiplicative Hankel forms associated with the Bergman spaces of Dirichlet series, reproducing most of the known results on multiplicative Hankel forms associated with the Hardy spaces of Dirichlet series. In addition, we find a direct relationship between the two type of forms which does not exist in lower dimensions. Finally, we produce some counter-examples concerning Carleson measures on the infinite polydisc.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/71182
Identification Number/DOI	10.1090/tran/7290
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	American Mathematical Society
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