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A characterization of bilinear forms on the dirichlet space
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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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CASCANTE, Ma. Carme (Maria Carme) and ORTEGA ARAMBURU, Joaquín M. A characterization of bilinear forms on the dirichlet space. Proceedings of the American Mathematical Society. 2012. Vol. 140, num. 7, pags. 2429-2440. ISSN 0002-9939. [consulted: 13 of June of 2026]. Available at: https://hdl.handle.net/2445/96825