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arXiv · 1311.1842

Extremal Domains for Self-Commutators in the Bergman Space

Matthew Fleeman·Dmitry Khavinson
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Abstract

In arXiv:1305.5193v1, the authors have shown that Putnam's inequality for the norm of self-commutators can be improved by a factor of $\frac{1}{2}$ for Toeplitz operators with analytic symbol $φ$ acting on the Bergman space $A^{2}(Ω)$. This improved upper bound is sharp when $φ(Ω)$ is a disk. In this paper we show that disks are the only domains for which the upper bound is attained.

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Matthew Fleeman, Dmitry Khavinson. 2013-11-07. Extremal Domains for Self-Commutators in the Bergman Space. https://arxiv.org/abs/1311.1842

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