scholarly journals Mixed norm Bergman–Morrey-type spaces on the unit disc

2016 ◽  
Vol 100 (1-2) ◽  
pp. 38-48 ◽  
Author(s):  
A. N. Karapetyants ◽  
S. G. Samko
Keyword(s):  
Unit Disc ◽  
Mixed Norm ◽  
Type Spaces

On mixed norm Bergman–Orlicz–Morrey spaces

2018 ◽  
Vol 25 (2) ◽  
pp. 271-282 ◽  
Author(s):  
Alexey N. Karapetyants ◽  
Stefan G. Samko
Keyword(s):  
Unit Disc ◽  
Fourier Coefficients ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bergman Projection ◽  
Mixed Norm ◽  
Taylor Coefficients ◽  
Type Spaces ◽  
Radial Variable

Abstract Following the ideas of our previous research, in this paper we continue the study of new Bergman-type spaces on the unit disc with mixed norm in terms of Fourier coefficients. Here we deal with the case where the sequence of norms of Fourier coefficients in the Orlicz–Morrey space in radial variable belongs to {l^{q}} . We study the boundedness of the Bergman projection and provide a description of functions in these spaces via the behavior of their Taylor coefficients.

scholarly journals On an Integral-Type Operator from Zygmund-Type Spaces to Mixed-Norm Spaces on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Type Operator ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Space ◽  
Mixed Norm Spaces ◽  
Norm Space ◽  
Type Spaces

The boundedness and compactness of an integral-type operator recently introduced by the author from Zygmund-type spaces to the mixed-norm space on the unit ball are characterized here.

scholarly journals Products of Composition and Differentiation between the Fractional Cauchy Spaces and the Bloch-Type Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
R. A. Hibschweiler
Keyword(s):  
Unit Disc ◽  
Cauchy Transforms ◽  
Type Spaces ◽  
Cauchy Spaces

The operators D C Φ and C Φ D are defined by D C Φ f = f ∘ Φ ′ and C Φ D f = f ′ ∘ Φ where Φ is an analytic self-map of the unit disc and f is analytic in the disc. A characterization is provided for boundedness and compactness of the products of composition and differentiation from the spaces of fractional Cauchy transforms F α to the Bloch-type spaces B β , where α > 0 and β > 0 . In the case β < 2 , the operator D C Φ : F α ⟶ B β is compact ⇔ D C Φ : F α ⟶ B β is bounded ⇔ Φ ′ ∈ B β , Φ Φ ′ ∈ B β and Φ ∞ < 1 . For β < 1 , C Φ D : F α ⟶ B β is compact ⇔ C Φ D : F α ⟶ B β is bounded ⇔ Φ ∈ B β and Φ ∞ < 1 .

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.

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