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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a characterization of bilinear forms on the Dirichlet space
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by Carme Cascante and Joaquin M. Ortega PDF
Proc. Amer. Math. Soc. 140 (2012), 2429-2440 Request permission

Abstract:

Arcozzi, Rochberg, Sawyer and Wick obtained a characterization of the holomorphic functions $b$ such that the Hankel type bilinear form $T_{b}(f,g)= \int _{{\mathbb D}}(I+R)(fg)(z) \overline {(I+R)b(z)}dv(z)$ is bounded on ${\mathcal D}\times {\mathcal D}$, where ${\mathcal D}$ is the Dirichlet space. In this paper we give an alternative proof of this characterization which tries to understand the similarity with the results of Maz$’$ya and Verbitsky relative to the Schrödinger forms on the Sobolev spaces $L_2^1(\mathbb {R}^n)$.
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Additional Information
  • Carme Cascante
  • Affiliation: Departmento Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain
  • Email: cascante@ub.edu
  • Joaquin M. Ortega
  • Affiliation: Departmento Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain
  • Email: ortega@ub.edu
  • Received by editor(s): February 23, 2011
  • Published electronically: November 15, 2011
  • Additional Notes: The authors were partially supported by DGICYT Grant MTM2011-27932-C02-01, DURSI Grant 2009SGR 1303 and Grant MTM2008-02928-E
  • Communicated by: Richard Rochberg
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 2429-2440
  • MSC (2010): Primary 31C25, 31C15, 47B35
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11409-6
  • MathSciNet review: 2898705