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

Bo Berndtsson

Displaying similar documents to “The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman”

Extension and restriction of holomorphic functions

Klas Diederich, Emmanuel Mazzilli (1997)

Annales de l'institut Fourier

Similarity:

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.

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

Jim Arlebrink (1993)

Annales de l'institut Fourier

Similarity:

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 $ℂ^{2}$ .

On the continuous extension of holomorphic correspondences

F. Berteloot, A. Sukhov (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Weighted Sobolev spaces in complex ellipsoids

Joaquín M. Ortega, Joan Fàbrega (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree

Chin-Huei Chang, Hsuan-Pei Lee (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

The Hartogs Theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for $C^{k}$ $\bar{\partial}$ -closed forms at the critical degree, $0 \leq k \leq \infty$ (Theorem 1.1). Part of Frenkel’s lemma in $C^{k}$ category is also proved.

A remark on semiglobal existence for $\bar{\partial}$

Alberto Scalari (1997)

Rendiconti del Seminario Matematico della Università di Padova

Similarity:

Displaying similar documents to “The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman”

Extension and restriction of holomorphic functions

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

On the continuous extension of holomorphic correspondences

Weighted Sobolev spaces in complex ellipsoids

Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree

A remark on semiglobal existence for ∂ ¯

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

A remark on semiglobal existence for $\bar{\partial}$