On the boundedness of the differentiation operator between weighted spaces of holomorphic functions

Anahit Harutyunyan; Wolfgang Lusky

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Displaying similar documents to “On the boundedness of the differentiation operator between weighted spaces of holomorphic functions”

Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces

Alexander V. Abanin, Pham Trong Tien (2012)

Studia Mathematica

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We obtain, in terms of associated weights, natural criteria for compact embedding of weighted Banach spaces of holomorphic functions on a wide class of domains in the complex plane. Our study is based on a complete characterization of finite-dimensional weighted spaces and canonical weights for them. In particular, we show that for a domain whose complement is not a Painlevé null set each nontrivial space of holomorphic functions with O-growth condition is infinite-dimensional. ...

Isometries between spaces of weighted holomorphic functions

Christopher Boyd, Pilar Rueda (2009)

Studia Mathematica

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We study isometries between spaces of weighted holomorphic functions. We show that such isometries have a canonical form determined by a group of homeomorphisms of a distinguished subset of the range and domain. A number of invariants for these isometries are determined. For specific families of weights we classify the form isometries can take.

Erratum to: "Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces" (Studia Math. 213 (2012), 169-187)

Alexander V. Abanin, Pham Trong Tien (2013)

Studia Mathematica

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Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions

Wolf, Elke (2011)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 47B33, 47B38. Let f be an analytic self-map of the open unit disk D in the complex plane and y be an analytic map on D. Such maps induce a weighted composition operator followed by differentiation DCf, y acting between weighted Banach spaces of holomorphic functions. We characterize boundedness and compactness of such operators in terms of the involved weights as well as the functions f and y.

Weighted composition operators between weighted Banach spaces of holomorphic functions and weighted Bloch type space

Elke Wolf (2009)

Annales Polonici Mathematici

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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator $ψ C_{ϕ}$ acting between weighted Banach spaces of holomorphic functions and weighted Bloch type spaces. Under some assumptions on the weights we give a necessary as well as a sufficient condition for such an operator to be bounded resp. compact.

Weighted composition operators from generalized weighted Bergman spaces to weighted-type spaces.

Gu, Dinggui (2008)

Journal of Inequalities and Applications [electronic only]

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On the extension of L2 holomorphic functions III: negligible weights.

Takeo Ohsawa (1995)

Mathematische Zeitschrift

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Weighted Fréchet spaces of holomorphic functions

Elke Wolf (2006)

Studia Mathematica

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This article deals with weighted Fréchet spaces of holomorphic functions which are defined as countable intersections of weighted Banach spaces of type $H^{\infty}$ . We characterize when these Fréchet spaces are Schwartz, Montel or reflexive. The quasinormability is also analyzed. In the latter case more restrictive assumptions are needed to obtain a full characterization.

On some properties of a differential operator on the polydisk.

Shamoyan, Romi, Li, Songxiao (2008)

Banach Journal of Mathematical Analysis [electronic only]

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The $v$ -boundary of weighted spaces of holomorphic functions.

Boyd, Christopher, Rueda, Pilar (2005)

Annales Academiae Scientiarum Fennicae. Mathematica

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Extension of separately holomorphic functions-a survey 1899-2001

Peter Pflug (2003)

Annales Polonici Mathematici

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This note is an attempt to describe a part of the historical development of the research on separately holomorphic functions.

On the cyclic elements of the shift operator in a weighted anisotropic space of holomorphic function in the polydisc.

Shamoyan, F.A. (2005)

Zapiski Nauchnykh Seminarov POMI

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On weighted composition operators acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces

Elke Wolf (2011)

Annales Polonici Mathematici

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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator $ψ C_{ϕ}$ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ

Weighted integrals of holomorphic functions in the unit polydisc.

Stević, Stevo (2005)

Journal of Inequalities and Applications [electronic only]

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Extension of separately holomorphic functions defined in non-open sets in the infinite dimensional case

Ludwik M. Drużkowski (1983)

Annales Polonici Mathematici

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Bounded projections and decompositions in spaces of holomorphic functions

M. Mateljević (1986)

Matematički Vesnik

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The image of a finely holomorphic map is pluripolar

Armen Edigarian, Said El Marzguioui, Jan Wiegerinck (2010)

Annales Polonici Mathematici

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We prove that the image of a finely holomorphic map on a fine domain in ℂ is a pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic functions.

Intermediate holomorphy

M. Nikić (1988)

Matematički Vesnik

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Splitting of the ∂-complex in weighted spaces of square integrable functions.

Michael Langenbruch (1992)

Revista Matemática de la Universidad Complutense de Madrid

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