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2009-06-04

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/48984

Pointwise estimates for the Bergman kernel of the weighted Fock space

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http://dx.doi.org/10.1007/s12220-009-9083-x

Abstract

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^{2}(e^{-2\phi}) $ where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann equation and we characterize the compactness of this operator in terms of $\Delta\phi$.

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Funcions de variables complexes, Funcions holomorfes

Subject (English)

Functions of complex variables, Holomorphic functions

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Articles publicats en revistes (Matemàtiques i Informàtica)

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MARZO SÁNCHEZ, Jordi and ORTEGA CERDÀ, Joaquim. Pointwise estimates for the Bergman kernel of the weighted Fock space. Journal of Geometric Analysis. 2009. Vol. 19, num. 4, pags. 890-910. ISSN 1050-6926. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/48984

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