共查询到20条相似文献,搜索用时 250 毫秒
1.
Bo-Yong Chen 《Arkiv f?r Matematik》2013,51(2):269-291
We give first of all a new criterion for Bergman completeness in terms of the pluricomplex Green function. Among several applications, we prove in particular that every Stein subvariety in a complex manifold admits a Bergman complete Stein neighborhood basis, which improves a theorem of Siu. Secondly, we give for hyperbolic Riemann surfaces a sufficient condition for when the Bergman and Poincaré metrics are quasi-isometric. A consequence is an equivalent characterization of uniformly perfect planar domains in terms of growth rates of the Bergman kernel and metric. Finally, we provide a noncompact Bergman complete pseudoconvex manifold without nonconstant negative plurisubharmonic functions. 相似文献
2.
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
3.
We prove that if D is a pseudoconvex domain with Lipschitz boundary having an exhaustion function such that is plurisubharmonic, then the Bergman projection maps the Sobolev space boundedly to itself for any .
Received March 10, 1999 / Published online May 8, 2000 相似文献
4.
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.
5.
For an arbitrary unimodular Lie group G, we construct strongly continuous unitary representations in the Bergman space of a strongly pseudoconvex neighborhood of G in the complexification of its underlying manifold. These representation spaces are infinite-dimensional and have compact kernels. In particular, the Bergman spaces of these natural manifolds are infinite-dimensional. 相似文献
6.
Xiangdong Yang 《Central European Journal of Mathematics》2013,11(1):74-84
We characterize the Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains in terms of the Berezin transform. 相似文献
7.
Steven G. Krantz 《Complex Analysis and Operator Theory》2014,8(2):571-579
We use Stokes’s theorem to establish an explicit and concrete connection between the Bergman and Szeg? projections on the disc, the ball, and on strongly pseudoconvex domains. 相似文献
8.
Miroslav Engliš 《Journal of Functional Analysis》2008,255(6):1419-1457
For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the reproducing kernels of Sobolev spaces of holomorphic functions of any real order. This generalizes the classical result of Fefferman for the unweighted Bergman kernel. Finally, we also exhibit a holomorphic continuation of the kernels with respect to the Sobolev parameter to the entire complex plane. Our main tool are the generalized Toeplitz operators of Boutet de Monvel and Guillemin. 相似文献
9.
Kenneth D. Koenig 《Mathematische Annalen》2007,339(3):667-693
We prove that the difference between the Bergman and Szegö projections on a bounded, pseudoconvex domain (with C ∞ boundary) is smoothing whenever the boundary Laplacian is subelliptic. An equivalent statement is that the Bergman projection can be represented as a composition of the Szegö and harmonic Bergman projections (along with the restriction and Poisson extension operators) modulo an error that is smoothing. We give several applications to the study of optimal mapping properties for these projections and their difference. 相似文献
10.
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
11.
本文对一类拟凸域E(m,n,K)给出其不变Kahler度量下的全纯截曲率的显表达式,并构造了E(m,n,K)的一个不变的完备的Kahler度量,使得它大于或等于Bergman度量,而且其全纯截曲率的上界是一个负常数,从而得到E(m,n,K)的Bergman度量和Kobayashi度量的比较定理。 相似文献
12.
We consider the Bergman projection on Henkin–Leiterer domains, bounded strictly pseudoconvex domains which have defining functions whose gradient is allowed to vanish. Our result describes the mapping properties of the Bergman projection between weighted Lp spaces, with the weights being powers of the gradient of the defining function. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
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
14.
Regularity and irregularity of the Bergman projection on \(L^p\) spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable \(\gamma \). A surprising consequence of the analysis is that, whenever \(\gamma \) is irrational, the Bergman projection is bounded only for \(p=2\). 相似文献
15.
M. Jasiczak 《Archiv der Mathematik》2006,87(5):436-448
We study regularity of Bergman and Szeg? projections on Sobolev type weighted-sup spaces. The paper covers the case of strongly
pseudoconvex domains with C4 boundary and, partially, domains of finite type in the sense of D’Angelo.
Received: 6 October 2005 相似文献
16.
Krantz Steven G. Li Song-Ying Rochberg Richard 《Integral Equations and Operator Theory》1997,28(2):196-213
The characterization of thosef for which the Hankel operatorsH
f belongs to various trace ideals over Bergman spaces on pseudoconvex domains of finite type in complex dimension two is given. In particular, we determine how the cutoff values are affected by the boundary geometry.All three authors supported by grants from the National Science Foundation 相似文献
17.
The nontangential behavior of the Bergman metric near a smooth convex boundary point of a bounded pseudoconvex domain D
n
is studied in terms of its multitype.Received January 25, 2002; in revised form June 20, 2002
Published online November 18, 2002 相似文献
18.
Zbigniew Blocki 《Transactions of the American Mathematical Society》2005,357(7):2613-2625
We improve a lower bound for the Bergman distance in smooth pseudoconvex domains due to Diederich and Ohsawa. As the main tool we use the pluricomplex Green function and an -estimate for the -operator of Donnelly and Fefferman.
19.
N. A. Shirokov 《Journal of Mathematical Sciences》1997,87(5):3925-3940
Denote by Kω(z, ζ) the Bergman kernel of a pseudoconvex domain Ω. For some classes of domains Ω, a relationship is found between the rate
of increase of Kω(z, z) as z tends to ∂Ω, and a purely geometric property of Ω. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 222, 1995, pp. 222–245. 相似文献
20.
Siqi Fu 《Journal of Geometric Analysis》2014,24(1):32-46
Estimates of the Bergman kernel and the Bergman and Kobayashi metrics on pseudoconvex domains near boundaries with constant Levi ranks are given. As a consequence, a characterization of Levi-flatness in terms of boundary behavior of the Bergman and Kobayashi metrics is obtained. 相似文献