대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제45권2호
  • /
  • Pages.321-338
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  • 2008
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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EXPLICIT SOBOLEV ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS

  • 발행 : 2008.05.31
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⟨ 이전 논문 다음 논문 ⟩

초록

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.

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참고문헌

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피인용 문헌

  1. HÖLDER ESTIMATES FOR THE CAUCHY-RIEMANN EQUATION ON PARAMETERS vol.48, pp.2, 2011, https://doi.org/10.4134/JKMS.2011.48.2.241
  2. SOBOLEV ESTIMATES FOR THE LOCAL EXTENSION OF BOUNDARY HOLOMORPHIC FORMS ON REAL HYPERSURFACES IN ℂn vol.50, pp.3, 2013, https://doi.org/10.4134/JKMS.2013.50.3.479