Covariant derivatives of the Berezin transform
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- by Miroslav Engliš and Renata Otáhalová PDF
- Trans. Amer. Math. Soc. 363 (2011), 5111-5129 Request permission
Abstract:
Improving upon recent results of Coburn, Xia, Li, Engliš and Zhang, Bommier-Hato, and others, we give estimates for higher-order covariant derivatives of the Berezin transform of bounded linear operators on a reproducing kernel Hilbert space of holomorphic functions. The answer turns out to involve the curvature of the Bergman-type metric associated to the reproducing kernel.References
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Additional Information
- Miroslav Engliš
- Affiliation: Mathematics Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic – and – Mathematics Institute, Academy of Sciences, Žitná 25, 11567 Prague 1, Czech Republic
- Email: englis{@}math.cas.cz
- Renata Otáhalová
- Affiliation: Mathematics Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic
- Email: Renata.Otahalova@math.slu.cz
- Received by editor(s): May 16, 2008
- Received by editor(s) in revised form: May 17, 2009
- Published electronically: May 4, 2011
- Additional Notes: This research was supported by GA AV ČR grant no. IAA100190802 and Ministry of Education research plan no. MSM4781305904
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 5111-5129
- MSC (2000): Primary 47B32; Secondary 32A36, 53B35, 32Q15
- DOI: https://doi.org/10.1090/S0002-9947-2011-05111-1
- MathSciNet review: 2813410