Sharp Berezin Lipschitz estimates

Coburn, L.

doi:10.1090/S0002-9939-06-08569-8

Sharp Berezin Lipschitz estimates
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by L. A. Coburn

Proc. Amer. Math. Soc. 135 (2007), 1163-1168

DOI: https://doi.org/10.1090/S0002-9939-06-08569-8

Published electronically: October 13, 2006

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Abstract:

F.A. Berezin introduced a general “symbol calculus" for linear operators on reproducing kernel Hilbert spaces. For the Segal-Bargmann space $H^2(\mathbf {C}^n,d\mu )$ of Gaussian square-integrable entire functions on complex $n$-space, $\mathbf {C}^n$, or for the Bergman spaces $A^2 (\Omega )$ of Euclidean volume square-integrable holomorphic functions on bounded domains $\Omega$ in $\mathbf {C}^n$, we show here that earlier Lipschitz estimates for Berezin symbols of arbitrary bounded operators are sharp.

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