Generalized Composition Operators Between Mixed-Norm and Some Weighted Spaces

2008 ◽  
Vol 29 (7-8) ◽  
pp. 959-978 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Composition Operators ◽  
Weighted Spaces ◽  
Mixed Norm

Adjoint of generalized Cesáro operators on analytic function spaces

2020 ◽  
Vol 26 (2) ◽  
pp. 185-192
Author(s):  
Sunanda Naik ◽  
Pankaj K. Nath
Keyword(s):  
Analytic Function ◽  
Convolution Operator ◽  
Composition Operators ◽  
Mixed Norm ◽  
Averaging Operators ◽  
Mixed Norm Spaces ◽  
Cesaro Averaging ◽  
Analytic Function Spaces ◽  
Appl Math ◽  
Two Parameter

AbstractIn this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular, we obtain a well-known result on the boundedness of composition operators given by Avetisyan and Stević in [K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 2009, 2, 304–311]. Also we consider the adjoint {\mathcal{A}^{b,c}} for {b>0} of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces {B_{\alpha+(c-1)}^{p,q}} for {c>1}.

Composition operators on weighted spaces of holomorphic functions on the upper half plane

2018 ◽  
Vol 122 (1) ◽  
pp. 141
Author(s):  
Wolfgang Lusky
Keyword(s):  
Half Plane ◽  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Bounded Operator ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Weight Functions ◽  
Spaces Of Holomorphic Functions ◽  
Upper Half Plane

We consider moderately growing weight functions $v$ on the upper half plane $\mathbb G$ called normal weights which include the examples $(\mathrm{Im} w)^a$, $w \in \mathbb G$, for fixed $a > 0$. In contrast to the comparable, well-studied situation of normal weights on the unit disc here there are always unbounded composition operators $C_{\varphi }$ on the weighted spaces $Hv(\mathbb G)$. We characterize those holomorphic functions $\varphi \colon \mathbb G \rightarrow \mathbb G$ where the composition operator $C_{\varphi } $ is a bounded operator $Hv(\mathbb G) \rightarrow Hv(\mathbb G)$ by a simple property which depends only on $\varphi $ but not on $v$. Moreover we show that there are no compact composition operators $C_{\varphi }$ on $Hv(\mathbb G)$.

scholarly journals Weighted Fractional Differentiation Composition Operators from Mixed-Norm Spaces to Weighted-Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
D. Borgohain ◽  
S. Naik
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Open Unit ◽  
Mixed Norm ◽  
Fractional Differentiation ◽  
Mixed Norm Space ◽  
Type Spaces ◽  
Analytic Maps ◽  
Weighted Type

Let 𝔻 be an open unit disc in the complex plane ℂ and let φ:𝔻→𝔻 as well as u:𝔻→ℂ be analytic maps. For an analytic function f(z)=∑n=0∞anzn on 𝔻 the weighted fractional differentiation composition operator is defined as (Dφ,uβf)(z)=u(z)f[β](φ(z)), where β≥0, f[β](z)=∑n=0∞(Γ(n+1+β)/Γ(n+1))anzn, and f0z=fz. In this paper, we obtain a characterization of boundedness and compactness of weighted fractional differentiation composition operator from mixed-norm space Hp,q,ϕ to weighted-type space Hμ∞.

scholarly journals New criteria for generalized weighted composition operators from mixed norm spaces into Zygmund-type spaces

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1171-1178
Author(s):  
Yong Ren
Keyword(s):  
Composition Operators ◽  
Mixed Norm ◽  
Weighted Composition Operators ◽  
Mixed Norm Spaces ◽  
Type Spaces ◽  
Weighted Composition ◽  
New Criteria ◽  
Generalized Weighted Composition Operators

New criteria for the boundedness and the compactness of the generalized weighted composition operators from mixed norm spaces into Zygmund-type spaces are given in this paper.

scholarly journals Weighted Iterated Radial Composition Operators between Some Spaces of Holomorphic Functions on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Mixed Norm ◽  
Mixed Norm Space ◽  
Type Space ◽  
Spaces Of Holomorphic Functions ◽  
Schmidt Norm ◽  
Norm Space ◽  
Weighted Type

The boundedness and compactness of weighted iterated radial composition operators from the mixed-norm space to the weighted-type space and the little weighted-type space on the unit ball are characterized here. We also calculate the Hilbert-Schmidt norm of the operator on the weighted Bergman-Hilbert space as well as on the Hardy space.

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