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arXiv · 0810.0388

Pointwise estimates for the Bergman kernel of the weighted Fock space

Jordi Marzo·Joaquim Ortega-Cerdá
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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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Jordi Marzo, Joaquim Ortega-Cerdá. 2008-10-02. Pointwise estimates for the Bergman kernel of the weighted Fock space. https://doi.org/10.1007/s12220-009-9083-x

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