Compact composition operators on Besov spaces

All entire functions which transform a class of holomorphic Zygmund-type spaces into weighted analytic Bloch space using the so-called n -generalized superposition operator are characterized in this paper. Moreover, certain specific properties such as boundedness and compactness of the newly defined class of generalized integral superposition operators are discussed and established by using the concerned entire functions.

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“…Therefore, in view of Lemma 3.7 in [17], we infer that the n-generalized superposition operator S g,n…”

Section: Lemmamentioning

confidence: 80%

“…Proof. Now, the concerned assertions ( 7), ( 9), and (11) of Lemma 3.7 in [17] can be satisfied for the analytic-type B ν space. In view of Lemma 7, thus, it is clear to show that the concerned assertions (i) and (ii) hold.…”

Section: Lemmamentioning

confidence: 95%

Integral Superposition-Type Operators on Some Analytic Function Spaces

Ahmed

Omran

2021

Journal of Function Spaces

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“…The following lemma follows by standard arguments similar to those outline in [13]. Hence, we omit the proof.…”

Section: 2 (2020)mentioning

confidence: 91%

D-metric Spaces and Composition Operators Between Hyperbolic Weighted Family of Function Spaces

Kamal

Yassen²

2020

Cubo

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The aim of this paper is to introduce new hyperbolic classes of functions, which will be called B * α, log and F * log (p, q, s) classes. Furthermore, we introduce D-metrics space in the hyperbolic type classes B * α, log and F * log (p, q, s). These classes are shown to be complete metric spaces with respect to the corresponding metrics. Moreover, necessary and sufficient conditions are given for the composition operator C φ to be bounded and compact from B * α, log to F * log (p, q, s) spaces. RESUMEN El objetivo de este artículo es introducir nuevas clases hiperbólicas de funciones, que serán llamadas clases B * α, log y F * log (p, q, s). A continuación, introducimos D-espacios métricos en las clases de tipo hiperbólicas B * α, log y F * log (p, q, s). Mostramos que estas clases son espacios métricos completos con respecto a las métricas correspondientes. Más aún, damos condiciones necesarias y suficientes para que el operador composición C φ sea acotado y compacto desde el espacio B * α, log a F * log (p, q, s).

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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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Compact composition operators on Besov spaces

Cited by 96 publications

References 10 publications

Integral Superposition-Type Operators on Some Analytic Function Spaces

Integral Superposition-Type Operators on Some Analytic Function Spaces

D-metric Spaces and Composition Operators Between Hyperbolic Weighted Family of Function Spaces

Holomorphic Hölder‐type spaces and composition operators

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