Abstract
In Olsen and Reguera (arXiv:1305.5193v1, 2013), 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 \(\varphi \) acting on the Bergman space \(A^{2}(\Omega )\). This improved upper bound is sharp when \(\varphi (\Omega )\) 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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Communicated by Mihai Putinar.
The authors acknowledge support from the NSF Grant DMS—0855597.
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Fleeman, M., Khavinson, D. Extremal Domains for Self-Commutators in the Bergman Space. Complex Anal. Oper. Theory 9, 99–111 (2015). https://doi.org/10.1007/s11785-014-0379-x
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DOI: https://doi.org/10.1007/s11785-014-0379-x