Pointwise estimates for the Bergman kernel of the weighted Fock space

Details Pointwise estimates for the Bergman kernel of the weighted Fock space Pointwise estimates for the Bergman kernel of the weighted Fock space

2008-10-02

arxiv.org/abs/0810.0388v1

Journal of Geometric Analysis: Volume 19, Issue 4 (2009), pp. 890-910

Mathematics

Complex Variables

Scientific paper

10.1007/s12220-009-9083-x

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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