Local Boundary Regularity of the Szego Projection and Biholomorphic Mappings of Non-Pseudoconvex Domains

Ma, Peiming

doi:10.1090/S0002-9947-98-01908-4

Local Boundary Regularity of the Szego Projection and Biholomorphic Mappings of Non-Pseudoconvex Domains
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by Peiming Ma

Trans. Amer. Math. Soc. 350 (1998), 419-428

DOI: https://doi.org/10.1090/S0002-9947-98-01908-4

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Abstract:

It is shown that the Szegő projection $S$ of a smoothly bounded domain $\Omega$, not necessarily pseudoconvex, satisfies local regularity estimates at certain boundary points, provided that condition $R$ holds for $\Omega$. It is also shown that any biholomorphic mapping $f:\Omega \rightarrow D$ between smoothly bounded domains extends smoothly near such points, provided that a weak regularity assumption holds for $D$.

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