Results 41 to 50 of about 217,307 (157)
On some extremal problems in Bergman spaces in weakly pseudoconvex domains [PDF]
, 2018 summary:We consider and solve extremal problems in various bounded weakly pseudoconvex domains in $\mathbb {C}^{n}$ based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces $A_{\alpha }^{p}$ in such type
Mihić, Olivera R. +2 more
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On the p-essential normality of principal submodules of the Bergman module on strongly pseudoconvex domains [PDF]
Advances in Mathematics, 2017 In this paper, we show that under a mild condition, a principal submodule of the Bergman module on a bounded strongly pseudoconvex domain with smooth boundary in $\mathbb{C}^n$ is $p$-essentially normal for all $p>n$. This is a significant improvement of
R. Douglas, K. Guo, Yi Wang
semanticscholar +1 more source
On isometries of the Carathéodory and Kobayashi metrics on strongly pseudoconvex domains
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2009 Summary: Let \(\Omega_1\) and \(\Omega_2\) be strongly pseudoconvex domains in \(\mathbb{C}^n\) and \(f:\Omega_1\to\Omega_2\) an isometry for the Kobayashi or Carathéodory metrics. Suppose that \(f\) extends as a \(C^1\) map to \(\overline\Omega\). We then prove that \(f|_{\partial \Omega_1}:\partial\Omega 1\to\partial\Omega_2\) is a CR or anti-CR ...
Seshadri, Harish, Verma, Kaushal
openaire +4 more sources
Estimates on the Bergman Kernels in a Tangential Direction on Pseudoconvex Domains in C3
Abstract and Applied Analysis, Volume 2018, Issue 1, 2018., 2018 Let Ω be a smoothly bounded pseudoconvex domain in C3 and assume that TΩreg(z0)<∞ where z0 ∈ bΩ, the boundary of Ω. Then we get optimal estimates of the Bergman kernel function along some “almost tangential curve” Cb(z0, δ0) ⊂ Ω ∪ {z0}.
Sanghyun Cho, Milan Pokorny
wiley +1 more source
On Traces in Some Analytic Spaces in Bounded Strictly Pseudoconvex Domains
Journal of Function Spaces, Volume 2015, Issue 1, 2015., 2015 New sharp estimates of traces of Bergman type spaces of analytic functions in bounded strictly pseudoconvex domains are obtained. These are, as far as we know, the first results of this type which are valid for any bounded strictly pseudoconvex domains with smooth boundary.
Romi F. Shamoyan +2 more
wiley +1 more source
Approximation of holomorphic mappings on strongly pseudoconvex domains [PDF]
Forum Mathematicum, 2008 Let D be a relatively compact strongly pseudoconvex domain in a Stein manifold, and let Y be a complex manifold. We prove that the set A(D,Y), consisting of all continuous maps from the closure of D to Y which are holomorphic in D, is a complex Banach manifold.
Drinovec-Drnovšek, Barbara +1 more
openaire +3 more sources
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 Let Ω be a smoothly bounded pseudoconvex domain in Cn with one degenerate eigenvalue and assume that there is a smooth holomorphic curve V whose order of contact with bΩ at z0 ∈ bΩ is larger than or equal to η. We show that the maximal gain in Hölder regularity for solutions of the ∂¯‐equation is at most 1/η.
Sanghyun Cho +2 more
wiley +1 more source
Global Regularity for the ∂-b‐Equation on CR Manifolds of Arbitrary Codimension
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Let M be a C∞ compact CR manifold of CR‐codimension l≥1 and CR‐dimension n-l in a complex manifold X of complex dimension n ≥ 3. In this paper, assuming that M satisfies condition Y(s) for some s with 11≤s≤n-l-, we prove an L2‐existence theorem and global regularity for the solutions of the tangential Cauchy‐Riemann equation for (0, s)‐forms on M.
Shaban Khidr +2 more
wiley +1 more source
Essential Norm Estimates of Weighted Composition Operators Between Bergman Spaces on Strongly Pseudoconvex Domains [PDF]
, 2007 We give estimates of the essential norms of weighted composition operators acting between Bergman spaces on strongly pseudoconvex domains.
Zhao, Ruhan, Cuckovic, Zeljko
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Journal of Function Spaces, Volume 2014, Issue 1, 2014., 2014 Weak‐star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak‐star closures of the corresponding bands of measures are reducing.
Marek Kosiek +2 more
wiley +1 more source