Contractive inequalities for Bergman spaces and multiplicative Hankel forms
Abstract
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.
Keywords
Cite
@article{arxiv.1701.06897,
title = {Contractive inequalities for Bergman spaces and multiplicative Hankel forms},
author = {Frédéric Bayart and Ole Fredrik Brevig and Antti Haimi and Joaquim Ortega-Cerdà and Karl-Mikael Perfekt},
journal= {arXiv preprint arXiv:1701.06897},
year = {2018}
}
Comments
This paper has been accepted for publication in Transactions of the AMS