共查询到20条相似文献,搜索用时 15 毫秒
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A stability theorem of the Bergman kernel and completeness of the Bergman metric have been proved on a type of non-smooth
pseudoconvex domains defined in the following way:D = {z∈U|r(z)} <whereU is a neighbourhood of
andr is a continuous plurisubharmonic function onU. A continuity principle of the Bergman Kernel for pseudoconvex domains with Lipschitz boundary is also given, which answers
a problem of Boas. 相似文献
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The Bergman kernel and biholomorphic mappings of pseudoconvex domains 总被引:10,自引:0,他引:10
Charles Fefferman 《Inventiones Mathematicae》1974,26(1):1-65
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The Bergman kernel function of some Reinhardt domains 总被引:5,自引:0,他引:5
The boundary behavior of the Bergman Kernel function of some Reinhardt domains is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points . Let be the Reinhardt domain
where , ; and let be the Bergman kernel function of . Then there exist two positive constants and and a function such that
holds for every . Here
and is the defining function for . The constants and depend only on and , not on .
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Sanghyun Cho 《Journal of Mathematical Analysis and Applications》2003,283(2):386-397
Let Ω be a smoothly bounded pseudoconvex domain in and let be a point of finite type. We also assume that the Levi form of bΩ is comparable in a neighborhood of z0. Then we get a quantity which bounds from above and below the Bergman kernel function in a small constant and large constant sense. 相似文献
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R. Michael Range 《Mathematische Annalen》2013,356(2):793-808
A new explicit construction of Cauchy–Fantappié kernels is introduced for an arbitrary weakly pseudoconvex domain with smooth boundary. While not holomorphic in the parameter, the new kernel reflects the complex geometry and the Levi form of the boundary. Some estimates are obtained for the corresponding integral operator, which provide evidence that this kernel and related constructions give useful new tools for complex analysis on this general class of domains. 相似文献
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Mathematische Annalen - 相似文献
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Arkadiusz Lewandowski 《Archiv der Mathematik》2018,111(5):503-511
We give the parameter version of a localization theorem for the Bergman metric near the boundary points of strictly pseudoconvex domains. The approximation theorem for square integrable holomorphic functions on such domains in the spirit of Graham-Kerzman is proved in the hereby paper, as well. 相似文献
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Huiping Li 《Integral Equations and Operator Theory》1994,19(4):458-476
We characterize functions fL
2(D) such that the Hankel operators Hf are, respectively, bounded and compact on the Bergman spaces of bounded strongly pseudoconvex domains.Research partially supported by a grant of the National Science Foundation. 相似文献
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Given a bounded strongly pseudoconvex domain D in with smooth boundary, we characterize ‐Bergman Carleson measures for , , and . As an application, we show that the Bergman space version of the balayage of a Bergman Carleson measure on D belongs to BMO in the Kobayashi metric. 相似文献
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Shi Jihuai 《中国科学A辑(英文版)》1998,41(1):22-32
A necessary and sufficient condition for the boundedness of the operator: $(T_{s,u,u} f)(\xi ) = h^{u + \tfrac{v}{a}} (\xi )\smallint _{\Omega _a } h^s (\xi ')K_{s,u,v} (\xi ,\xi ')f(\xi ')dv(\xi ') on L^p (\Omega _a ,dv_\lambda ),1< p< \infty $ , is obtained, where $\Omega _a = \left\{ {\xi = (z,w) \in \mathbb{C}^{n + m} :z \in \mathbb{C}^n ,w \in \mathbb{C}^m ,|z|^2 + |w|^{2/a}< 1} \right\},h(\xi ) = (1 - |z|^2 )^a - |w|^2 $ andK x,u,v (ξ,ξ′).This generalizes the works in literature from the unit ball or unit disc to the weakly pseudoconvex domain ω a . As an appli cation, it is proved thatf?L H p (ω a ,dv λ) implies $h\tfrac{{|a|}}{a} + |\beta |(\xi )D_2^a D_z^\beta f \in L^p (\Omega _a ,dv_\lambda ),1 \leqslant p< \infty $ , for any multi-indexa=(α1,?,α n and ß = (ß1, —ß). An interesting question is whether the converse holds. 相似文献
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Galia Dafni 《Journal of Geometric Analysis》1994,4(3):273-316
We consider Hardy spacesH p,p ≤ 1, of holomorphic functions in the interior of Ω. where Ω is either a strongly pseudoconvex domain inC n or a weakly pseudoconvex domain of finite type inC 2. We exhibit an atomic decomposition for the boundary values of these functions (in the sense of distributions), thus showing that they belong to the local real Hardy spacesh p(?Ω). 相似文献
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Bo-Yong Chen 《Proceedings of the American Mathematical Society》2006,134(1):139-148
We prove a localization principle of the Bergman kernel form and metric for pseudoconvex domains in the complex projective space. An estimate of the Bergman distance is also given.
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We get the Bergman kernel functions in explicit formulas on four types of Hua domain.There are two key steps: First, we give the holomorphic automorphism groups of four types of Hua domain; second, we introduce the concept of semi-Reinhardt domain and give their complete orthonormal systems. Based on these two aspects we obtain the Bergman kernel function in explicit formulas on Hua domains. 相似文献