Weighted reproducing kernels and Toeplitz operators on harmonic Bergman spaces on the real ball
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- by Renata Otáhalová
- Proc. Amer. Math. Soc. 136 (2008), 2483-2492
- DOI: https://doi.org/10.1090/S0002-9939-08-09384-2
- Published electronically: March 7, 2008
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Abstract:
For the standard weighted Bergman spaces on the complex unit ball, the Berezin transform of a bounded continuous function tends to this function pointwise as the weight parameter tends to infinity. We show that this remains valid also in the context of harmonic Bergman spaces on the real unit ball of any dimension. This generalizes the recent result of C. Liu for the unit disc, as well as the original assertion concerning the holomorphic case. Along the way, we also obtain a formula for the corresponding weighted harmonic Bergman kernels.References
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Bibliographic Information
- Renata Otáhalová
- Affiliation: Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic
- Email: Renata.Otahalova@math.slu.cz
- Received by editor(s): March 5, 2007
- Published electronically: March 7, 2008
- Additional Notes: This research was supported by projects 201/03/H152 from the Grant Agency of the Czech Republic, and MSM 4781305904 from the Czech Ministry of Education.
- Communicated by: Michael T. Lacey
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2483-2492
- MSC (2000): Primary 47B35; Secondary 32A25, 31B05, 33C55
- DOI: https://doi.org/10.1090/S0002-9939-08-09384-2
- MathSciNet review: 2390517