Pseudolocal estimates for \(\overline\partial\) on general pseudoconvex domains. (English) Zbl 1044.32029

Author’s abstract: “Extending the well-known results for smoothly bounded case, we show that subelliptic and pseudolocal estimates hold in the neighbourhood of a smooth strictly pseudoconvex (or finite type) boundary point of any pseudoconvex domain (i.e., possibly, unbounded or with nonsmooth boundary). As an application, we also prove the corresponding generalization of Kerzman’s and Fefferman-Boutet de Monvel-Sjöstrand’s results on the boundary behaviour of the Bergman kernel.”
This paper is well written and well organized; it provides a useful reference for many topics related to the \(\overline\partial\)-Neumann problem on (possibly) unbounded and non-smooth psuedoconvex domains.


32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
32T15 Strongly pseudoconvex domains
32T25 Finite-type domains
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