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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Contractive inequalities for Bergman spaces and multiplicative Hankel forms
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by Frédéric Bayart, Ole Fredrik Brevig, Antti Haimi, Joaquim Ortega-Cerdà and Karl-Mikael Perfekt PDF
Trans. Amer. Math. Soc. 371 (2019), 681-707 Request permission


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.
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Additional Information
  • Frédéric Bayart
  • Affiliation: Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
  • MR Author ID: 683115
  • Email:
  • Ole Fredrik Brevig
  • Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
  • MR Author ID: 1069722
  • Email:
  • Antti Haimi
  • Affiliation: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
  • MR Author ID: 1040783
  • Email:
  • Joaquim Ortega-Cerdà
  • Affiliation: Department de Matemàtiques i Informàtica, Universitat de Barcelona & Barcelona Graduate school in mathematics, Gran Via 585, 08007 Barcelona, Spain
  • ORCID: 0000-0002-6616-4257
  • Email:
  • Karl-Mikael Perfekt
  • Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996
  • Email:
  • Received by editor(s): January 31, 2017
  • Received by editor(s) in revised form: May 9, 2017, and May 10, 2017
  • Published electronically: August 21, 2018
  • Additional Notes: The second-named author was supported by Grant 227768 of the Research Council of Norway. The third-named author was supported by Lise Meitner grant of Austrian Science Fund (FWF). The fourth-named author was supported by the MTM2014-51834-P grant by the Ministerio de Economía y Competitividad, and by the Generalitat de Catalunya (project 2014 SGR 289).
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 681-707
  • MSC (2010): Primary 30H20; Secondary 47B35, 30B50
  • DOI:
  • MathSciNet review: 3885157