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Bergman Subspaces and Subkernels: Degenerate \(L^p\) Mapping and Zeroes

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Abstract

Regularity and irregularity of the Bergman projection on \(L^p\) spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable \(\gamma \). A surprising consequence of the analysis is that, whenever \(\gamma \) is irrational, the Bergman projection is bounded only for \(p=2\).

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Acknowledgements

Research of the second author was partially supported by a National Science Foundation grant.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA

    L. D. Edholm

  2. Department of Mathematics, The Ohio State University, Columbus, OH, USA

    J. D. McNeal

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  1. L. D. Edholm
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  2. J. D. McNeal
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Correspondence to J. D. McNeal.

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Edholm, L.D., McNeal, J.D. Bergman Subspaces and Subkernels: Degenerate \(L^p\) Mapping and Zeroes. J Geom Anal 27, 2658–2683 (2017). https://doi.org/10.1007/s12220-017-9777-4

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  • DOI: https://doi.org/10.1007/s12220-017-9777-4

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