Local boundary regularity of the Bergman projection in non-pseudoconvex domains
Abstract
The local boundary regularity problem of the Bergman projection and kernel function is studied for smoothly bounded domains which are not necessarily pseudoconvex. Certain type of boundary points are defined to be extreme, which are present for any smoothly bounded domain. And it is shown that near these points the Bergman projection is regular, in the sense that certain pseudolocal estimates are satisfied. As a consequence, it is also proved that the Bergman kernel function extends smoothly to the boundary in one of the variables while the other variable is fixed in the domain. Moreover, if the Bergman projection is globally regular, then all the Sobolev space projections as well as the Szego projection are locally regular at extreme boundary points. If the extreme boundary point is further assumed to be strictly pseudoconvex near which the boundary of the domain is real analytic, then the Bergman kernel function has a holomorphic extension past the point.
Degree
Ph.D.
Advisors
Bell, Purdue University.
Subject Area
Mathematics
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