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Pointwise estimates for the Bergman kernel of the weighted Fock space

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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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Versió postprint del document publicat a: DOI 10.1007/s12220-009-9083-x

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Journal of Geometric Analysis, 2009, vol. 19, num. 4, p. 890-910

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Pointwise estimates for the Bergman kernel of the weighted Fock space