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Approximation of holomorphic mappings on strongly pseudoconvex domains [PDF]
Forum Mathematicum, 2009 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 ...
Barbara Drinovec-Drnovšek +11 more
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Strongly pseudoconvex domains as subvarieties of complex manifolds
American Journal of Mathematics, 2009 In this paper (a sequel to B. Drinovec Drnovsek and F. Forstneric, Holomorphic curves in complex spaces, Duke Math. J. 139 (2007), 203-253) we obtain existence and approximation results for closed complex subvarieties that are normalized by strongly ...
Drnovsek, Barbara Drinovec +1 more
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Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2020 The purpose of the note is to obtain equivalent quasinorm, sharp estimates for the quasinorm of Hardy’s and new Bergman’s analytic classes of in the polydisk.
Shamoyan, R.F., Tomashevskaya, E.B.
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Comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains [PDF]
, 2018 We prove that for a strongly pseudoconvex domain $D\subset\mathbb C^n$, the infinitesimal Carath\'eodory metric $g_C(z,v)$ and the infinitesimal Kobayashi metric $g_K(z,v)$ coincide if $z$ is sufficiently close to $bD$ and if $v$ is sufficiently close to
Bracci, Filippo +2 more
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The corona problem with two pieces of data [PDF]
, 2010 We study the corona problem on the unit ball in $\CC^n$, and more generally on strongly pseudoconvex domains in $\CC^n$. When the corona problem has just two pieces of data, and an extra geometric hypothesis is satisfied, then we are able to solve ...
Krantz, Steven G.
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Geometric properties of semitube domains [PDF]
, 2014 In the paper we study the geometry of semitube domains in $\mathbb C^2$. In particular, we extend the result of Burgu\'es and Dwilewicz for semitube domains dropping out the smoothness assumption.
Kosiński, Łukasz +2 more
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Strongly pseudoconvex handlebodies
, 2003 We give an explicit construction of special strongly pseudoconvex domains in C^n of handlebody type, i.e., domains which are small tubes surrounding the union of a quadratic strongly pseudoconvex domain with an attached totally real handle.
Forstneric, Franc, Kozak, Jernej
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Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains
, 2009 We characterize using the Bergman kernel Carleson measures of Bergman spaces in strongly pseudoconvex bounded domains in several complex variables, generalizing to this setting theorems proved by Duren and Weir for the unit ball.
Abate, Marco, Saracco, Alberto
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Regularity of Kobayashi metric
, 2018 We review some recent results on existence and regularity of Monge-Amp\`ere exhaustions on the smoothly bounded strongly pseudoconvex domains, which admit at least one such exhaustion of sufficiently high regularity.
A Newlander +17 more
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ON TRACES OF ANALYTIC HERZ AND BLOCH TYPE SPACES IN BOUNDED STRONGLY PSEUDOCONVEX DOMAINS IN C^N
Проблемы анализа, 2014 In our paper we provide some direct extentions of our recent sharp results on traces in the analytic function spaces, which we proved earlier in case of the unit ball in C^n, to the case of the bounded strongly pseudoconvex domains with a smooth boundary.
R. F. Shamoyan, S. M. Kurilenko
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