EXPLICIT SOBOLEV ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS

Title & Authors
EXPLICIT SOBOLEV ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS
Cho, Sang-Hyun; Choi, Jae-Seo;

Abstract
Let $\small{\bar{M}}$ be a smoothly bounded pseudoconvex complex manifold with a family of almost complex structures $\small{\{L^{\tau}\}_{{\tau}{\in}I}}$, $\small{0{\in}I}$, which extend smoothly up to bM, the boundary of M, and assume that there is $\small{{\lambda}{\in}C^{\infty}}$(bM) which is strictly subharmonic with respect to the structure $\small{L^0|_{bM}}$ in any direction where the Levi-form vanishes on bM. We obtain explicit estimates for the $\small{\bar{\partial}}$-Neumann problem in Sobolev spaces both in space and parameter variables. Also we get a similar result when $\small{\bar{M}}$ is strongly pseudoconvex.
Keywords
Cauchy Riemann equations;Sobolev estimates;
Language
English
Cited by
1.
HÖLDER ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS,;

대한수학회지, 2011. vol.48. 2, pp.241-252
2.
SOBOLEV ESTIMATES FOR THE LOCAL EXTENSION OF BOUNDARY HOLOMORPHIC FORMS ON REAL HYPERSURFACES IN ℂn,;

대한수학회지, 2013. vol.50. 3, pp.479-491
1.
HÖLDER ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS, Journal of the Korean Mathematical Society, 2011, 48, 2, 241
2.
SOBOLEV ESTIMATES FOR THE LOCAL EXTENSION OF BOUNDARY HOLOMORPHIC FORMS ON REAL HYPERSURFACES IN ℂn, Journal of the Korean Mathematical Society, 2013, 50, 3, 479
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