Extremal Domains for Self-Commutators in the Bergman Space
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 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 )...
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| Veröffentlicht in: | Complex analysis and operator theory 2015-01, Vol.9 (1), p.99-111 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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
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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| ISSN: | 1661-8254 1661-8262 |
| DOI: | 10.1007/s11785-014-0379-x |