Peak functions on convex domains

Kolář, Martin

Displaying similar documents to “Peak functions on convex domains”

The pluricomplex Green function on some regular pseudoconvex domains

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 $_{D} (z, w)$ 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.

Quantitative estimates for the Green function and an application to the Bergman metric

Klas Diederich, Gregor Herbort (2000)

Annales de l'institut Fourier

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Let $D \subset ℂ^{n}$ be a bounded pseudoconvex domain that admits a Hölder continuous plurisubharmonic exhaustion function. Let its pluricomplex Green function be denoted by $G_{D} (., .)$ . In this article we give for a compact subset $K \subset D$ a quantitative upper bound for the supremum ${sup}_{z \in K} | G_{D} (z, w) |$ in terms of the boundary distance of $K$ and $w$ . This enables us to prove that, on a smooth bounded regular domain $D$ (in the sense of Diederich-Fornaess), the Bergman differential metric $B_{D} (w; X)$ tends to infinity, for $X \in ℂ^{n} / {O}$ , when $w \in D$ tends to a boundary...

The $\bar{\partial}$ -Neumann operator on Lipschitz $q$ -pseudoconvex domains

Sayed Saber (2011)

Czechoslovak Mathematical Journal

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On a bounded $q$ -pseudoconvex domain $Ω$ in $ℂ^{n}$ with a Lipschitz boundary, we prove that the $\bar{\partial}$ -Neumann operator $N$ satisfies a subelliptic $(1 / 2)$ -estimate on $Ω$ and $N$ can be extended as a bounded operator from Sobolev $(- 1 / 2)$ -spaces to Sobolev $(1 / 2)$ -spaces.

On boundary behaviour of the Bergman projection on pseudoconvex domains

M. Jasiczak (2005)

Studia Mathematica

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It is shown that on strongly pseudoconvex domains the Bergman projection maps a space $L v_{k}$ 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 $E \supset L^{\infty} (Ω)$ defined by weighted-sup seminorms and equipped...

$L ²_{h}$ -domains of holomorphy and the Bergman kernel

Peter Pflug, Włodzimierz Zwonek (2002)

Studia Mathematica

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We give a characterization of $L ²_{h}$ -domains of holomorphy with the help of the boundary behavior of the Bergman kernel and geometric properties of the boundary, respectively.

Proper holomorphic liftings and new formulas for the Bergman and Szegő kernels

E. H. Youssfi (2002)

Studia Mathematica

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We consider a large class of convex circular domains in $M_{m ₁, n ₁} (ℂ) \times . . . \times M_{m_{d}, n_{d}} (ℂ)$ which contains the oval domains and minimal balls. We compute their Bergman and Szegő kernels. Our approach relies on the analysis of some proper holomorphic liftings of our domains to some suitable manifolds.

On some new sharp embedding theorems in minimal and pseudoconvex domains

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 $ℂ^{n} .$ 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...

Global boundary regularity for the $\bar{p a r t i a l}$ -equation on $q$ -pseudo-convex domains

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 $D$ of $C^{n}$ , we introduce a notion of « $q$ -pseudoconvexity» of new type and prove that for a given $\bar{\partial}$ -closed $(p, r)$ -form $f$ that is smooth up to the boundary on $D$ , and for $r \geq q$ , there exists a $(p, r - 1)$ -form $u$ smooth up to the boundary on $D$ which is a solution of the equation $\bar{\partial} u = f$

Analytic extension from non-pseudoconvex boundaries and $A (D)$ -convexity

Christine Laurent-Thiébaut, Egmon Porten (2003)

Annales de l’institut Fourier

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Let $D \subset \subset ℂ^{n}, n \geq 2$ , be a domain with $C^{2}$ -boundary and $K \subset \partial D$ be a compact set such that $\partial D ∖ K$ is connected. We study univalent analytic extension of CR-functions from $\partial D ∖ K$ to parts of $D$ . Call $K$ CR-convex if its $A (D)$ -convex hull, $A (D) - hull (K)$ , satisfies $K = \partial D \cap A (D) - hull (K)$ ( $A (D)$ denoting the space of functions, which are holomorphic on $D$ and continuous up to $\partial D$ ). The main theorem of the paper gives analytic extension to $\partial D ∖ A (D) - hull (K)$ , if $K$ is CR- convex.