Henkin-Ramirez formulas with weight factors

B. Berndtsson; Mats Andersson

Displaying similar documents to “Henkin-Ramirez formulas with weight factors”

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in $ℂ^{2}$

Jim Arlebrink (1993)

Annales de l'institut Fourier

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Let $D$ be a bounded strictly pseudoconvex domain in $ℂ^{2}$ and let $X$ be a positive divisor of $D$ with finite area. We prove that there exists a bounded holomorphic function $f$ such that $X$ is the zero set of $f$ . This result has previously been obtained by Berndtsson in the case where $D$ is the unit ball in $ℂ^{2}$ .

Extension and restriction of holomorphic functions

Klas Diederich, Emmanuel Mazzilli (1997)

Annales de l'institut Fourier

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Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds $D^{'}$ of pseudoconvex domains $D$ to all of $D$ even in quite simple situations; The spaces $A^{p} (D^{'}) : = 𝒪 (D^{'}) \cap L^{p} (D^{'})$ are, in general, not at all preserved. Also the image of the Hilbert space $A^{2} (D)$ under the restriction to $D^{'}$ can have a very strange structure.

The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman

Bo Berndtsson (1996)

Annales de l'institut Fourier

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We give a short proof of the extension theorem of Ohsawa-Takegoshi. The same method also gives a generalization of the $\overline{\partial}$ -theorem of Donnelly and Fefferman for the case of $(n, 1)$ -forms.

Peak functions on convex domains

Kolář, Martin

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Let $Ω \subset ℂ^{n}$ be a domain with smooth boundary and $p \in \partial Ω$ . A holomorphic function $f$ on $Ω$ is called a $C^{k}$ ( $k = 0, 1, 2, \dots$ ) peak function at $p$ if $f \in C^{k} (\bar{Ω})$ , $f (p) = 1$ , and $| f (q) | < 1$ for all $q \in \bar{Ω} ∖ {p}$ . If $Ω$ is strongly pseudoconvex, then $C^{\infty}$ peak functions exist. On the other hand, J. E. Fornaess constructed an example in $ℂ^{2}$ to show that this result fails, even for $C^{1}$ 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...

Displaying similar documents to “Henkin-Ramirez formulas with weight factors”

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in ℂ 2

Extension and restriction of holomorphic functions

The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman

Peak functions on convex domains

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in $ℂ^{2}$