Abstract
We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in L 2(e −2φ) where φ is a subharmonic function with Δφ 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 Δφ.
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Communicated by Kang-Tae Kim.
Supported by projects MTM2008-05561-C02-01 and 2005SGR00611.
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Marzo, J., Ortega-Cerdà, J. Pointwise Estimates for the Bergman Kernel of the Weighted Fock Space. J Geom Anal 19, 890–910 (2009). https://doi.org/10.1007/s12220-009-9083-x
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DOI: https://doi.org/10.1007/s12220-009-9083-x