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Title: A characterization of bilinear forms on the dirichlet space
Author: Cascante, Ma. Carme (Maria Carme)
Ortega Aramburu, Joaquín M.
Keywords: Teoria del potencial (Matemàtica)
Teoria d'operadors
Operadors lineals
Potential theory (Mathematics)
Operator theory
Linear operators
Issue Date: Jul-2012
Publisher: American Mathematical Society (AMS)
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)(f,g)(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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It is part of: Proceedings of the American Mathematical Society, 2012, vol. 140, num. 7, p. 2429-2440
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ISSN: 0002-9939
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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