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 $L_2^1(\mathbb {R}^n)$.References
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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