Compact Toeplitz Operators for Weighted Bergman Spaces on Bounded Symmetric Domains |
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Authors: | Hassan Issa |
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Institution: | (1) Department of Mathematics, University of Jammu, Jammu, 180 006, India |
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Abstract: | Let
W ì \mathbb Cd{\Omega \subset{\mathbb C}^{d}} be an irreducible bounded symmetric domain of type (r, a, b) in its Harish–Chandra realization. We study Toeplitz operators Tng{T^{\nu}_{g}} with symbol g acting on the standard weighted Bergman space Hn2{H_\nu^2} over Ω with weight ν. Under some conditions on the weights ν and ν
0 we show that there exists C(ν, ν
0) > 0, such that the Berezin transform (g)\tilde]n0{\tilde{g}_{\nu_{0}}} of g with respect to H2n0{H^2_{\nu_0}} satisfies:
\labele0||(g)\tilde]n0||¥ £ C(n,n0)||Tng||,\label{e0}\|\tilde{g}_{\nu_0}\|_\infty \leq C(\nu,\nu_0)\|T^\nu_g\|, |
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Keywords: | |
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