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Korenblum constants for some function spaces


Authors: Wee JunJie and Le Hai Khoi
Journal: Proc. Amer. Math. Soc. 148 (2020), 1175-1185
MSC (2010): Primary 30H20, 46E15
DOI: https://doi.org/10.1090/proc/14778
Published electronically: September 23, 2019
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Abstract: We study the Korenblum Maximum Principle on the weighted Fock spaces and the weighted Bergman spaces with exponential weights. First, we give explicit expressions for the upper bounds of Korenblum constants for the weighted Fock spaces. Then, we obtain upper bounds of such constants for the weighted Bergman spaces. Finally, we show a failure of the Korenblum Maximum Principle for weighted Bergman spaces $ A^p_\alpha (\mathbb{D})$, where $ 0<p<1$, $ \alpha >0$.


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Additional Information

Wee JunJie
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore
Email: weej0016@e.ntu.edu.sg

Le Hai Khoi
Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore
Email: lhkhoi@ntu.edu.sg

DOI: https://doi.org/10.1090/proc/14778
Keywords: Hardy space, Bergman space, Fock space, exponential weight, Korenblum constant
Received by editor(s): May 1, 2019
Received by editor(s) in revised form: July 18, 2019
Published electronically: September 23, 2019
Additional Notes: This work was supported in part by MOE’s AcRF Tier 1 grant M4011724.110 (RG128/16)
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2019 American Mathematical Society