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Comparing the Bergman and Szegö projections on domains with subelliptic boundary Laplacian

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Abstract

We prove that the difference between the Bergman and Szegö projections on a bounded, pseudoconvex domain (with C ∞ boundary) is smoothing whenever the boundary Laplacian is subelliptic. An equivalent statement is that the Bergman projection can be represented as a composition of the Szegö and harmonic Bergman projections (along with the restriction and Poisson extension operators) modulo an error that is smoothing. We give several applications to the study of optimal mapping properties for these projections and their difference.

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Authors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, OH, 43210, USA

    Kenneth D. Koenig

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  1. Kenneth D. Koenig
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Correspondence to Kenneth D. Koenig.

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Research supported in part by NSF Grants DMS–0400505 and DMS–0457500.

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Koenig, K.D. Comparing the Bergman and Szegö projections on domains with subelliptic boundary Laplacian. Math. Ann. 339, 667–693 (2007). https://doi.org/10.1007/s00208-007-0128-9

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  • DOI: https://doi.org/10.1007/s00208-007-0128-9

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