共查询到20条相似文献,搜索用时 15 毫秒
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Der-Chen E. Chang 《manuscripta mathematica》1988,62(4):437-447
In this paper, we discuss the relations between a special Heisenberg coordinate system and a normalized Levi metric on strongly pseudo-convex domains in Cn and see how they are related to the
-Neumann operator.Work supported by MSRI, Berkeley, California. 相似文献
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Claudio Rea 《Annali di Matematica Pura ed Applicata》1976,110(1):161-175
Sunto Si dimostra l'esistenza della soluzione per l'operatore di Cauchy-Riemann parametrizzato, nel caso continuo per varietà fortemente
pseudoconvesse e nel caso differenziabile per varietà di Stein.
Entrata in Redazione il 20 maggio 1975.
Supported by C.N.R. research groups. 相似文献
Entrata in Redazione il 20 maggio 1975.
Supported by C.N.R. research groups. 相似文献
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In this paper we obtain non-isotropic weighted L
p
estimates with the boundary distance weight function for the -equation on piecewise smooth strictly pseudoconvex domains under a hypothesis of complex transversality in ℂn using the explicit formula of solutions by Berndtsson-Andersson.
This work was supported by the Korea Research Foundation Grant funded by Korea Government (MOEHRD, Basic Research Promotion
Fund) (Grant No. KRF-2005-070-C00007) 相似文献
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Friedrich Haslinger 《Czechoslovak Mathematical Journal》2008,58(4):1247-1256
We prove that compactness of the canonical solution operator to restricted to (0, 1)-forms with holomorphic coefficients is equivalent to compactness of the commutator
defined on the whole L
(0,1)2(Ω), where is the multiplication by and is the orthogonal projection of L
(0,1)2(Ω) to the subspace of (0, 1) forms with holomorphic coefficients. Further we derive a formula for the -Neumann operator restricted to (0, 1) forms with holomorphic coefficients expressed by commutators of the Bergman projection
and the multiplications operators by z and .
Partially supported by the FWF grant P19147-N13. 相似文献
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Judith Brinkschulte 《Arkiv f?r Matematik》2004,42(2):259-282
We consider a domain Ω with Lipschitz boundary, which is relatively compact in ann-dimensional Kähler manifold and satisfies some “logδ-pseudoconvexity” condition. We show that the\(\bar \partial \)-equation with exact support in ω admits a solution in bidegrees (p, q), 1≤q≤n?1. Moreover, the range of\(\bar \partial \) acting on smooth (p, n?1)-forms with support in\(\bar \Omega \) is closed. Applications are given to the solvability of the tangential Cauchy-Riemann equations for smooth forms and currents for all intermediate bidegrees on boundaries of weakly pseudoconvex domains in Stein manifolds and to the solvability of the tangential Cauchy-Riemann equations for currents on Levi flatCR manifolds of arbitrary codimension. 相似文献
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Joe J. Perez 《Journal of Geometric Analysis》2009,19(1):87-106
Let G be a unimodular Lie group, X a compact manifold with boundary, and M be the total space of a principal bundle G→M→X so that M is also a strongly pseudoconvex complex manifold. In this work, we show that if G acts by holomorphic transformations in M, then the Laplacian
on M has the following properties: The kernel of □ restricted to the forms Λ
p,q
with q>0 is a closed, G-invariant subspace in L
2(M,Λ
p,q
) of finite G-dimension. Secondly, we show that if q>0, then the image of □ contains a closed, G-invariant subspace of finite G-codimension in L
2(M,Λ
p,q
). These two properties taken together amount to saying that □ is a G-Fredholm operator. It is a corollary of the first property mentioned that the reduced L
2-Dolbeault cohomology spaces
of M are finite G-dimensional for q>0. The boundary Laplacian □
b
has similar properties.
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Heungju Ahn 《Mathematische Nachrichten》2007,280(4):343-350
We introduce a notion of q ‐pseudoconvex domain of new type for a bounded domain of ?n and prove that for given a ‐closed (p, r)‐form, r ≥ q, that is smooth up to the boundary, there exists a (p, r – 1)‐form smooth up to the boundary which is a solution of ‐equation on a bounded q ‐pseudoconvex domain. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献