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- W4322620598 abstract "We prove a modified form of the classical Morrey-Kohn-Hormander identity, adapted to pseudoconcave boundaries. Applying this result to an annulus between two bounded pseudoconvex domains in $mathbb{C}^n$, where the inner domain has $mathcal{C}^{1,1}$ boundary, we show that the $L^2$ Dolbeault cohomology group in bidegree $(p,q)$ vanishes if $1leq qleq n-2$ and is Hausdorff and infinite-dimensional if $q=n-1$, so that the Cauchy-Riemann operator has closed range in each bidegree. As a dual result, we prove that the Cauchy-Riemann operator is solvable in the $L^2$ Sobolev space $W^1$ on any pseudoconvex domain with $mathcal{C}^{1,1}$ boundary. We also generalize our results to annuli between domains which are weakly $q$-convex in the sense of Ho for appropriate values of $q$." @default.
- W4322620598 created "2023-03-01" @default.
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- W4322620598 date "2018-11-08" @default.
- W4322620598 modified "2023-09-27" @default.
- W4322620598 title "A Modified Morrey-Kohn-Hormander Identity and Applications" @default.
- W4322620598 doi "https://doi.org/10.48550/arxiv.1811.03715" @default.
- W4322620598 hasPublicationYear "2018" @default.
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