Contractive inequalities for Bergman spaces and multiplicative Hankel forms
| Autor: | Ole Fredrik Brevig, Joaquim Ortega-Cerdà, Karl-Mikael Perfekt, Antti Haimi, Frédéric Bayart |
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| Přispěvatelé: | Universitat de Barcelona |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Inequality Function algebras Funcions de variables complexes General Mathematics media_common.quotation_subject Àlgebres de funcions Polydisc Type (model theory) Teoria d'operadors 01 natural sciences Functions of complex variables symbols.namesake 0103 physical sciences Analytic functions FOS: Mathematics Number Theory (math.NT) 0101 mathematics Dirichlet series media_common Mathematics Mathematics::Functional Analysis Mathematics - Number Theory Mathematics::Complex Variables Applied Mathematics 010102 general mathematics Multiplicative function Operator theory Hardy space Linear operators Functional Analysis (math.FA) Mathematics - Functional Analysis Funcions analítiques symbols 010307 mathematical physics Isoperimetric inequality Operadors lineals Unit (ring theory) |
| Zdroj: | Transactions of the American Mathematical Society Dipòsit Digital de la UB Universidad de Barcelona Recercat. Dipósit de la Recerca de Catalunya instname |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/tran/7290 |
| Popis: | 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. Comment: This paper has been accepted for publication in Transactions of the AMS |
| Databáze: | OpenAIRE |
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