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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Displaying similar documents to “Associated weights and spaces of holomorphic functions”
Splitting of the ∂-complex in weighted spaces of square integrable functions.
Regularity of general weighted inductive limits.
JOCHEN WENGENROTH (1999)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Biduality in (LF)-spaces.
Klaus D. Bierstedt, José Bonet (2001)
RACSAM
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En la Sección 1 se pueban resultados abstractos sobre preduales y sobre bidualidad de espacios (LF). Sea E = ind E un espacio (LF), ponemos H = ind H para una sucesión de subespacios de Fréchet H de E con H ⊂ H. Investigamos bajo qué condiciones el espacio E es canónicamente (topológicamente isomorfo a) el bidual inductivo (H')' o (incluso) al bidual fuerte de H. Los resultados abstractos se aplican en la Sección 2, especialmente a espacios (LF) ponderados de funciones holomorfas, pero...
On the boundedness of the differentiation operator between weighted spaces of holomorphic functions
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.
The -boundary of weighted spaces of holomorphic functions.
Boyd, Christopher, Rueda, Pilar (2005)
Annales Academiae Scientiarum Fennicae. Mathematica
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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. ...
Sequence space representations for (FN)-algebras of entire functions modulo closed ideals
Reinhold Meise, B. Taylor (1987)
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.
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 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 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.
A sequence space representation of the space of bounded ultradistributions of Beurling type.
María del Carmen Gómez-Collado (2002)
RACSAM
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Sequence space representations of the spaces D(R) and of its dual D'(R), the space of bounded ultradistributions of Beurling type, are presented, in case the weight ω is a strong weight.
On the "Fundamental Principle" of L. Ehrenpreis
Sönke Hansen (1983)
Banach Center Publications
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Henkin-Ramirez formulas with weight factors
B. Berndtsson, Mats Andersson (1982)
Annales de l'institut Fourier
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We construct a generalization of the Henkin-Ramírez (or Cauchy-Leray) kernels for the -equation. The generalization consists in multiplication by a weight factor and addition of suitable lower order terms, and is found via a representation as an “oscillating integral”. As special cases we consider weights which behave like a power of the distance to the boundary, like exp- with convex, and weights of polynomial decrease in . We also briefly consider kernels with singularities on...