scholarly journals On the dimension of the Fock type spaces

2021 ◽  
pp. 125288
Author(s):  
Alexander Borichev ◽  
Van An Le ◽  
El Hassan Youssfi
Keyword(s):  
Type Spaces

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

scholarly journals Improving KKM Theory on General Metric Type Spaces

2021 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
Sehie Park
Keyword(s):  
Convex Space ◽  
Metric Spaces ◽  
Space Theory ◽  
Type Space ◽  
Generalized Metric ◽  
Abstract Convex Space ◽  
Type Spaces

Abstract A generalized metric type space is a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them.

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

scholarly journals Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M

2019 ◽  
Vol 69 (6) ◽  
pp. 1367-1380 ◽  
Author(s):  
Stanislav Chaichenko ◽  
Andrii Shidlich ◽  
Fahreddin Abdullayev
Keyword(s):  
Fractional Order ◽  
Moduli Of Smoothness ◽  
Best Approximations ◽  
Approximation Theorems ◽  
Inverse Approximation ◽  
Type Spaces

Abstract In the Orlicz type spaces 𝓢M, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of smoothness and Peetre K-functionals in the spaces 𝓢M.

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