Weighted spaces of holomorphic functions on balanced domains.

Bierstedt, Klaus D.; Bonet, José; Galbis, Antonio

doi:10.1307/mmj/1029004753

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Introduction and Notation3

Preliminaries In the Following Let Us Denote By B The Open1

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Cited by 112 publications

(102 citation statements)

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“…This Banach space has been studied for instance in [3]. In particular, it is proved in [3, Theorem 1.5] that the polynomials are dense in Hv 0 (B).…”

Section: Preliminaries In the Following Let Us Denote By B The Openmentioning

confidence: 99%

Universal Radial Limits of Holomorphic Functions

Bayart¹

2005

Glasgow Math. J.

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Abstract. We investigate the radial behavior of holomorphic functions in the unit ball B of ‫ރ‬ n . In particular, we prove the existence of universal holomorphic functions f in the following sense : given any measurable function ϕ on ∂B, there is a sequence (r n ) n≥1 , 0 < r n < 1, that converges to 1, such that f (r n ξ ) converges to ϕ(ξ ) for almost every ξ ∈ ∂B.2000 Mathematics Subject Classification. 32A40.

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“…This Banach space has been studied for instance in [3]. In particular, it is proved in [3, Theorem 1.5] that the polynomials are dense in Hv 0 (B).…”

Section: Preliminaries In the Following Let Us Denote By B The Openmentioning

confidence: 99%

Universal Radial Limits of Holomorphic Functions

Bayart¹

2005

Glasgow Math. J.

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“…Hence, from the τ co -compactness of the closed unit ball and the τ co -continuity of T, [4] and [6]. It is a well-known fact that…”

Section: Proof the Equivalences (I)-(ii) And (Iii)-(iv) Follow From mentioning

confidence: 97%

“…The Cesàro means of the Taylor polynomials satisfy [4]. Clearly, changing the value of v on a compact interval does not change the spaces and gives an equivalent norm.…”

Section: Introduction and Notationmentioning

confidence: 99%

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Classical operators on weighted Banach spaces of entire functions

Beltrán¹,

Bonet²,

Fernández

2013

Proc. Amer. Math. Soc.

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“…The weighted space of holomorphic functions H [3], [4], [6], [13], [14], [16] and the references therein.…”

Section: Introduction Notation and Motivationmentioning

confidence: 99%

A Note on Completeness of Weighted Normed Spaces of Analytic Functions

Bonet

Vukotić

2017

Results Math

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Given a non-negative weight v, not necessarily bounded or strictly positive, defined on a domain G in the complex plane, we consider the weighted space H ∞ v (G) of all holomorphic functions on G such that the product v|f | is bounded in G and study the question of when such a space is complete under the canonical sup-seminorm. We obtain both some necessary and some sufficient conditions in terms of the weight v, exhibit several relevant examples, and characterize completeness in the case of spaces with radial weights on balanced domains.

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Weighted spaces of holomorphic functions on balanced domains.

Cited by 112 publications

References 0 publications

Universal Radial Limits of Holomorphic Functions

Universal Radial Limits of Holomorphic Functions

Classical operators on weighted Banach spaces of entire functions

A Note on Completeness of Weighted Normed Spaces of Analytic Functions

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