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Weighted reproducing kernels and Toeplitz operators on harmonic Bergman spaces on the real ball

Author: Renata Otáhalová
Journal: Proc. Amer. Math. Soc. 136 (2008), 2483-2492
MSC (2000): Primary 47B35; Secondary 32A25, 31B05, 33C55
Published electronically: March 7, 2008
MathSciNet review: 2390517
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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.

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Additional Information

Renata Otáhalová
Affiliation: Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic

Keywords: Reproducing kernel, Toeplitz operators, harmonic Bergman space.
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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