Let be a bounded Lipschitz q-pseudoconvex domain that admit good weight functions. We shall prove that the canonical solution operator for the -equation is compact on the boundary of and is bounded in the Sobolev space for some values of k. Moreover, we show that the Bergman projection and the -Neumann operator are bounded in the Sobolev space for some values of k. If is smooth, we shall give sufficient conditions for compactness of the -Neumann operator.
Submitted May 8, 2018. Published April 10, 2019.
Math Subject Classifications: 35J20, 35J25, 35J60.
Key Words: Lipschitz domain; q-pseudoconvex domain.
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| Sayed Saber |
Faculty of Science
Beni-Suef University, Egypt
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