Bergman projections on weighted Fock spaces in several complex variables

Let ϕ be a real-valued plurisubharmonic function on C n whose complex Hessian has uniformly comparable eigenvalues, and let F p ( ϕ ) be the Fock space induced by ϕ . In this paper, we conclude that the Bergman projection is bounded from the p th Lebesgue space L p ( ϕ ) to F p ( ϕ ) for 1 ≤ p ≤ ∞ ....

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2017; no. 1; pp. 286 - 10
Main Author: Lv, Xiaofen
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 2017
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Bergman kernel
Bergman projection
Complex variables
Eigenvalues
Mathematical analysis
Mathematics
Mathematics and Statistics
reverse-Hölder inequality
Bergman projection
reverse-Hölder inequality
Bergman kernel
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:Let ϕ be a real-valued plurisubharmonic function on C n whose complex Hessian has uniformly comparable eigenvalues, and let F p ( ϕ ) be the Fock space induced by ϕ . In this paper, we conclude that the Bergman projection is bounded from the p th Lebesgue space L p ( ϕ ) to F p ( ϕ ) for 1 ≤ p ≤ ∞ . As a remark, we claim that Bergman projections are also well defined and bounded on Fock spaces F p ( ϕ ) with 0 < p < 1 . We also obtain the estimates for the distance induced by ϕ and the L p ( ϕ ) -norm of Bergman kernel for F 2 ( ϕ ) .
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-017-1560-3