Contractive inequalities for Bergman spaces and multiplicative Hankel forms
Journal article, Peer reviewed
Accepted version
View/ Open
Date
2019Metadata
Show full item recordCollections
- Institutt for matematiske fag [2533]
- Publikasjoner fra CRIStin - NTNU [38576]
Original version
Transactions of the American Mathematical Society. 2019, 371 (1), 681-707. 10.1090/tran/7290Abstract
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 types of forms which does not exist in lower dimensions. Finally, we produce some counterexamples concerning Carleson measures on the infinite polydisc.