Displaying similar documents to “A generalization of Schwarz's lemma and of Hadamard's three circles theorem”

On D*-extension property of the Hartogs domains.

Do Duc Thai, Pascal J. Thomas (2001)

Publicacions Matemàtiques

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A complex analytic space is said to have the D*-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X x C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the function giving the logarithm of the reciprocal of the radius of the fibers, so that, when X is...

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 ' ) ∩ 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.

Behavior of holomorphic functions in complex tangential directions in a domain of finite type in C.

Sandrine Grellier (1992)

Publicacions Matemàtiques

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Let Ω be a domain in C. It is known that a holomorphic function on Ω behaves better in complex tangential directions. When Ω is of finite type, the best possible improvement is quantified at each point by the distance to the boundary in the complex tangential directions (see the papers on the geometry of finite type domains of Catlin, Nagel-Stein and Wainger for precise definition). We show that this improvement is characteristic: for a holomorphic function, a regularity in complex tangential...