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An integral kernel for weakly pseudoconvex domains

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Abstract

A new explicit construction of Cauchy–Fantappié kernels is introduced for an arbitrary weakly pseudoconvex domain with smooth boundary. While not holomorphic in the parameter, the new kernel reflects the complex geometry and the Levi form of the boundary. Some estimates are obtained for the corresponding integral operator, which provide evidence that this kernel and related constructions give useful new tools for complex analysis on this general class of domains.

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Notes

  1. \(\left|f\right|_{0}\) denotes the supremum norm of \(f\) over \(bD\).

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Authors and Affiliations

  1. Department of Mathematics, State University of New York at Albany, Albany, NY, 12222, USA

    R. Michael Range

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  1. R. Michael Range
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Correspondence to R. Michael Range.

Additional information

Part of this research was begun while the author was visiting at the University of Utah in Winter 2011. The author would like to thank the Mathematics Department of that University for the hospitality and support extended to him.

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Range, R.M. An integral kernel for weakly pseudoconvex domains. Math. Ann. 356, 793–808 (2013). https://doi.org/10.1007/s00208-012-0863-4

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  • DOI: https://doi.org/10.1007/s00208-012-0863-4

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