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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Alexander V. Abanin, Pham Trong Tien (2013)
Studia Mathematica
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Anahit Harutyunyan, Wolfgang Lusky (2008)
Studia Mathematica
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We give necessary and sufficient conditions on the weights v and w such that the differentiation operator D: Hv(Ω) → Hw(Ω) between two weighted spaces of holomorphic functions is bounded and onto. Here Ω = ℂ or Ω = 𝔻. In particular we characterize all weights v such that D: Hv(Ω) → Hw(Ω) is bounded and onto where w(r) = v(r)(1-r) if Ω = 𝔻 and w = v if Ω = ℂ. This leads to a new description of normal weights.
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.
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.
Thiago R. Alves (2014)
Studia Mathematica
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We show that if U is a domain of existence in a separable Banach space, then the set of holomorphic functions on U whose domain of existence is U is lineable and algebrable.
P. Pflug (1985)
Matematički Vesnik
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Elke Wolf (2009)
Annales Polonici Mathematici
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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator 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.
Shamoyan, Romi, Li, Songxiao (2008)
Banach Journal of Mathematical Analysis [electronic only]
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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.
M. Nikić (1988)
Matematički Vesnik
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Ludwik M. Drużkowski (1983)
Annales Polonici Mathematici
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Boyd, Christopher, Rueda, Pilar (2005)
Annales Academiae Scientiarum Fennicae. Mathematica
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Takeo Ohsawa (1995)
Mathematische Zeitschrift
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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.
Harris, Lawrence A. (2003)
Abstract and Applied Analysis
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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 . 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.
Verónica Dimant, Pablo Galindo, Manuel Maestre, Ignacio Zalduendo (2004)
Studia Mathematica
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We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Fréchet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity.
Tran Ngoc Giao (1994)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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