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Title: Contractive inequalitie for Bergman spaces and multiplicative Hankel forms.
Author: Bayart, Frédéric
Brevig, Ole Fredrik
Haimi, Antti
Ortega Cerdà, Joaquim
Perfekt, Karl-Mikael
Keywords: Funcions de variables complexes
Àlgebres de funcions
Funcions analítiques
Operadors lineals
Teoria d'operadors
Functions of complex variables
Function algebras
Analytic functions
Linear operators
Operator theory
Issue Date: Jan-2019
Publisher: American Mathematical Society (AMS)
Abstract: Abstract. We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimet- ric inequality and of Weissler's inequality for dilations. By contractivity and a standard tensorization procedure, the unit disc inequalities yield correspond- ing 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 multi- plicative 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.
Note: Reproducció del document publicat a:
It is part of: Transactions of the American Mathematical Society, 2019, vol. 371, num. 1, p. 681-707
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ISSN: 0002-9947
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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