Compactness of the canonical solution operator on Lipschitz q-pseudoconvex boundaries
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Date
2019-04-10
Authors
Saber, Sayed
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
Let Ω ⊂ ℂn be a bounded Lipschitz q-pseudoconvex domain that admit good weight functions. We shall prove that the canonical solution operator for the the ∂¯-equation is compact on the boundary of Ω and is bounded in the Sobolev space Wkr,s(Ω) for some values of k. Moreover, we show that the Bergman projection and the ∂¯-Neumann operator are bounded in the Sobolev space Wkr,s(Ω) for some values of k. If Ω is smooth, we shall give sufficient conditions for compactness of the ∂¯-Neumann operator.
Description
Keywords
Lipschitz domain, q-Pseudoconvex domain
Citation
Saber, S. (2019). Compactness of the canonical solution operator on Lipschitz q-pseudoconvex boundaries. <i>Electronic Journal of Differential Equations, 2019</i>(48), pp. 1-22.
Rights
Attribution 4.0 International