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\noindent Let $\Omega $ be a smoothly bounded pseudoconvex domain in $\cn $ and assume that the $(n-2)$-eigenvalues of the Levi-form are comparable in a neighborhood of $z_0\in \bo$. Also, assume that there is a smooth 1-dimensional analytic variety $V$ whose order of contact with $\bo$ at $z_0$ is equal to $\eta$ and $\Delta_{n-2}(z_0)<\infty$. We show that the maximal gain in H\"older regularity for solutions of the $\dbar$-equation is at most $\frac {1}{\eta}$.
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참고문헌 (14)
참고문헌 신청
David W. Catlin / 1989 / Estimates of invariant metrics on pseudoconvex domains of dimension two / Mathematische Zeitschrift 200(3):429~466
Sanghyun Cho / 1992 / Extension of complex structures on weakly pseudoconvex compact complex manifolds with boundary / Mathematische Zeitschrift 211(1):105~119
Sanghyun Cho / 1992 / A lower bound on the Kobayashi metric near a point of finite type in ℂ n / Journal of Geometric Analysis 2(4):317~325
Sanghyun Cho / 2002 / Estimates of invariant metrics on pseudoconvex domains with comparable Levi form / Kyoto Journal of Mathematics 42(2):337~349
Sanghyun Cho / 2003 / Boundary behavior of the Bergman kernel function on pseudoconvex domains with comparable Levi form / Journal of Mathematical Analysis and Applications 283(2):386~397
Sanghyun Cho / 1992 / Extension of complex structures on weakly pseudoconvex compact complex manifolds with boundary / Mathematische Zeitschrift 211(1):105~119
Sanghyun Cho / 1992 / A lower bound on the Kobayashi metric near a point of finite type in ℂ n / Journal of Geometric Analysis 2(4):317~325
Sanghyun Cho / 2002 / Estimates of invariant metrics on pseudoconvex domains with comparable Levi form / Kyoto Journal of Mathematics 42(2):337~349
Sanghyun Cho / 2003 / Boundary behavior of the Bergman kernel function on pseudoconvex domains with comparable Levi form / Journal of Mathematical Analysis and Applications 283(2):386~397
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