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http://dx.doi.org/10.4134/BKMS.2008.45.2.321

EXPLICIT SOBOLEV ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS  

Cho, Sang-Hyun (Department of Mathematics Sogang University)
Choi, Jae-Seo (Department of Mathematics Sogang University)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 321-338 More about this Journal
Abstract
Let $\bar{M}$ be a smoothly bounded pseudoconvex complex manifold with a family of almost complex structures $\{L^{\tau}\}_{{\tau}{\in}I}$, $0{\in}I$, which extend smoothly up to bM, the boundary of M, and assume that there is ${\lambda}{\in}C^{\infty}$(bM) which is strictly subharmonic with respect to the structure $L^0|_{bM}$ in any direction where the Levi-form vanishes on bM. We obtain explicit estimates for the $\bar{\partial}$-Neumann problem in Sobolev spaces both in space and parameter variables. Also we get a similar result when $\bar{M}$ is strongly pseudoconvex.
Keywords
Cauchy Riemann equations; Sobolev estimates;
Citations & Related Records

Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
연도 인용수 순위
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