Saber, Sayed2021-11-052021-11-052019-04-10Saber, S. (2019). Compactness of the canonical solution operator on Lipschitz q-pseudoconvex boundaries. <i>Electronic Journal of Differential Equations, 2019</i>(48), pp. 1-22.1072-6691https://hdl.handle.net/10877/14781Let 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.Text22 pages1 file (.pdf)enAttribution 4.0 InternationalLipschitz domainq-Pseudoconvex domainArticle