Small sets of infinite type are benign for the \overline∂-Neumann problem

Boas, Harold P.

doi:10.1090/S0002-9939-1988-0943086-2

Small sets of infinite type are benign for the $\overline \partial$-Neumann problem
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by Harold P. Boas

Proc. Amer. Math. Soc. 103 (1988), 569-578

DOI: https://doi.org/10.1090/S0002-9939-1988-0943086-2

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Abstract:

An explicit construction shows that the $\bar \partial$-Neumann operator and the Bergman and Szegő projections are globally regular in every smooth bounded pseudoconvex domain whose set of boundary points of infinite type has Hausdorff two-dimensional measure equal to zero. On the other hand there are examples of domains with globally regular $\bar \partial$-Neumann operator but whose infinite-type points fill out an open subset of the boundary.

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