Composition operators on the weighted Bloch space and the weighted Dirichlet spaces, and<i>BMOA</i>with closed range

Yoneda, Rikio

doi:10.1080/17476933.2017.1345887

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…Examples of such functions are 1 (r)∶=r , 𝛼 > 0 , 2 ∶=r ln(2∕r) and 3 (r)∶=r ln(1 − r) , 𝛽 > 1 , for r ∈ (0, 1] (see [22, p. 110]) and with (z) = 1 (1 − |z| 2 ) = (1 − |z| 2 ) , z ∈ , one gets Theorem 4.7 back for ≥ 1 . For 0 < 𝛼 < 1 and (z) = 1 (1 − |z| 2 ) , z ∈ , the equivalence (i) ⇔ (ii) is given in [47, Proposition 4.4, p. 14] of Yoneda as well and a sufficient condition implying (ii) in [47,Corollary 4.5,p.15]. Ramos-Fernández generalises the results given in [22] to bounded essential weights on by [41,Theorem 4.3,p.…”

Section: E Has Closed Range) (Ii)mentioning

confidence: 99%

Extension of vector-valued functions and weak–strong principles for differentiable functions of finite order

Kruse

2021

Ann. Funct. Anal.

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In this paper we study the problem of extending functions with values in a locally convex Hausdorff space E over a field $$\mathbb {K}$$ K , which has weak extensions in a weighted Banach space $${\mathcal {F}}\nu (\Omega ,\mathbb {K})$$ F ν ( Ω , K ) of scalar-valued functions on a set $$\Omega$$ Ω , to functions in a vector-valued counterpart $$\mathcal {F}\nu (\Omega ,E)$$ F ν ( Ω , E ) of $${\mathcal {F}}\nu (\Omega ,\mathbb {K})$$ F ν ( Ω , K ) . Our findings rely on a description of vector-valued functions as continuous linear operators and extend results of Frerick, Jordá and Wengenroth. As an application we derive weak-strong principles for continuously partially differentiable functions of finite order and vector-valued versions of Blaschke’s convergence theorem for several spaces.

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Section: E Has Closed Range) (Ii)mentioning

confidence: 99%

Extension of vector-valued functions and weak–strong principles for differentiable functions of finite order

Kruse

2021

Ann. Funct. Anal.

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“…The study of the boundedness and compactness of the composition operator C ϕ in various function spaces over the unit disc and more general domains is a classical problem studied by many researchers. Without claiming for completeness, we mention the following spaces and references: the Besov space, 1‐4 Bloch space

scriptB

, 5‐8 Dirichlet space

scriptD

, 9‐15 BMOA, 7,8,16‐18 Hardy space H p , 19‐24 Bergman space

{scriptA}^{p}

and the weighted Bergman space

{scriptA}_{α}^{p}

, 19,20,25 Fock space, 26‐29 among others.…”

Section: Introductionmentioning

confidence: 99%

Holomorphic Hölder‐type spaces and composition operators

Karapetyants

Restrepo

2020

Math Methods in App Sciences

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We study boundedness and compactness of composition operators in the generalized Hölder-type space of holomorphic functions in the unit disc with prescribed modulus of continuity. We also devote a significant part of the article to outline some embeddings between such Hölder-type spaces, to discuss properties of modulus of continuity and to construct some useful examples. KEYWORDS composition operators, Hölder spaces, holomorphic functions, modulus of continuity MSC CLASSIFICATION 47B33; 46E15; 30H99 1 INTRODUCTION Let D stand for the unit disc in complex plane C. Given a holomorphic function ∶ D → D by C , we denote the linear composition operator C f(z) ∶= f• (z) = f((z)). The study of the boundedness and compactness of the composition operator C in various function spaces over the unit disc and more general domains is a classical problem studied by many researchers. Without claiming for completeness, we mention the following spaces and references: the Besov space, 1-4

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Closed Range Composition Operators on BMOA

Erdem

Tjani

2021

Complex Anal. Oper. Theory

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Composition operators on the weighted Bloch space and the weighted Dirichlet spaces, andBMOAwith closed range

Cited by 3 publications

References 9 publications

Extension of vector-valued functions and weak–strong principles for differentiable functions of finite order

Extension of vector-valued functions and weak–strong principles for differentiable functions of finite order

Holomorphic Hölder‐type spaces and composition operators

Closed Range Composition Operators on BMOA

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