-estimates for the Cauchy-Riemann equations on certain weakly pseudoconvex domains
Jerzy Ryczaj (1987)
Colloquium Mathematicae
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Jerzy Ryczaj (1987)
Colloquium Mathematicae
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Gregor Herbort (2014)
Annales Polonici Mathematici
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Let D be a smooth bounded pseudoconvex domain in ℂⁿ of finite type. We prove an estimate on the pluricomplex Green function of D that gives quantitative information on how fast the Green function vanishes if the pole w approaches the boundary. Also the Hölder continuity of the Green function is discussed.
M. Jasiczak (2005)
Studia Mathematica
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It is shown that on strongly pseudoconvex domains the Bergman projection maps a space of functions growing near the boundary like some power of the Bergman distance from a fixed point into a space of functions which can be estimated by the consecutive power of the Bergman distance. This property has a local character. Let Ω be a bounded, pseudoconvex set with C³ boundary. We show that if the Bergman projection is continuous on a space defined by weighted-sup seminorms and equipped...
Kolář, Martin
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Let be a domain with smooth boundary and . A holomorphic function on is called a () peak function at if , , and for all . If is strongly pseudoconvex, then peak functions exist. On the other hand, J. E. Fornaess constructed an example in to show that this result fails, even for functions, on a weakly pseudoconvex domain [Math. Ann. 227, 173-175 (1977; Zbl 0346.32026)]. Subsequently, E. Bedford and J. E. Fornaess showed that there is always a continuous peak function...
Peter Pflug, Włodzimierz Zwonek (2002)
Studia Mathematica
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We give a characterization of -domains of holomorphy with the help of the boundary behavior of the Bergman kernel and geometric properties of the boundary, respectively.
Sayed Saber (2011)
Czechoslovak Mathematical Journal
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On a bounded -pseudoconvex domain in with a Lipschitz boundary, we prove that the -Neumann operator satisfies a subelliptic -estimate on and can be extended as a bounded operator from Sobolev -spaces to Sobolev -spaces.
Marco M. Peloso, Hercule Valencourt (2010)
Colloquium Mathematicae
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We study the boundary behaviour of holomorphic functions in the Hardy-Sobolev spaces , where is a smooth, bounded convex domain of finite type in ℂⁿ, by describing the approach regions for such functions. In particular, we extend a phenomenon first discovered by Nagel-Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains.
Piotr Jakóbczak (1988)
Annales Polonici Mathematici
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Romi F. Shamoyan, Olivera R. Mihić (2016)
Czechoslovak Mathematical Journal
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We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our...
Klas Diederich, Gregor Herbort (2000)
Annales de l'institut Fourier
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Let be a bounded pseudoconvex domain that admits a Hölder continuous plurisubharmonic exhaustion function. Let its pluricomplex Green function be denoted by . In this article we give for a compact subset a quantitative upper bound for the supremum in terms of the boundary distance of and . This enables us to prove that, on a smooth bounded regular domain (in the sense of Diederich-Fornaess), the Bergman differential metric tends to infinity, for , when tends to a boundary...
Heungju Ahn (2005)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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For a bounded domain of , we introduce a notion of «-pseudoconvexity» of new type and prove that for a given -closed -form that is smooth up to the boundary on , and for , there exists a -form smooth up to the boundary on which is a solution of the equation