scholarly journals Integral operator acting on weighted Dirichlet spaces to Morrey type spaces

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3723-3736
Author(s):  
Liu Yang
Keyword(s):  
Integral Operator ◽  
Carleson Measure ◽  
Integral Operators ◽  
Essential Norm ◽  
Dirichlet Spaces ◽  
Type Spaces ◽  
Weighted Dirichlet Spaces

In this paper, we studied the boundedness and compactedness of integral operators from weighted Dirichlet spaces DK to Morrey type spaces H2K. Carleson measure and essential norm were also considered.

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.

Carleson measure and Volterra type operators on weighted BMOA spaces

2020 ◽  
Vol 27 (3) ◽  
pp. 413-424
Author(s):  
Ruishen Qian ◽  
Songxiao Li
Keyword(s):  
Unit Disk ◽  
Carleson Measure ◽  
Borel Measure ◽  
Integral Operators ◽  
Volterra Type ◽  
Bmoa Spaces ◽  
Type Spaces

AbstractLet μ be a nonnegative Borel measure on the unit disk {\mathbb{D}}. In this paper, we investigate measures μ such that the weighted {\mathrm{BMOA}} spaces are embedded boundedly or compactly into tent-type spaces {\mathcal{T}_{\varphi}^{\infty}(\mu)}. As an application, we characterize the boundedness and compactness of Volterra integral operators on the weighted {\mathrm{BMOA}} space.

Embedding of Dirichlet type spaces into tent spaces and Volterra operators

2020 ◽  
pp. 1-12
Author(s):  
Ruishen Qian ◽  
Xiangling Zhu
Keyword(s):  
Integral Operators ◽  
Essential Norm ◽  
Function Spaces ◽  
General Function ◽  
Tent Spaces ◽  
Dirichlet Type ◽  
Volterra Operators ◽  
Type Spaces ◽  
Inclusion Mapping ◽  
Dirichlet Type Spaces

Abstract In this paper, we study the boundedness and compactness of the inclusion mapping from Dirichlet type spaces $\mathcal {D}^{p}_{p-1 }$ to tent spaces. Meanwhile, the boundedness, compactness, and essential norm of Volterra integral operators from Dirichlet type spaces $\mathcal {D}^{p}_{p-1 }$ to general function spaces are also investigated.

THE ESSENTIAL NORMS OF COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

2018 ◽  
Vol 97 (2) ◽  
pp. 297-307
Author(s):  
YUFEI LI ◽  
YUFENG LU ◽  
TAO YU
Keyword(s):  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Dirichlet Space ◽  
Essential Norm ◽  
Angular Derivative ◽  
Dirichlet Spaces ◽  
Closed Unit Disc ◽  
Weighted Dirichlet Spaces

Let $\unicode[STIX]{x1D711}$ be an analytic self-map of the unit disc. If $\unicode[STIX]{x1D711}$ is analytic in a neighbourhood of the closed unit disc, we give a precise formula for the essential norm of the composition operator $C_{\unicode[STIX]{x1D711}}$ on the weighted Dirichlet spaces ${\mathcal{D}}_{\unicode[STIX]{x1D6FC}}$ for $\unicode[STIX]{x1D6FC}>0$. We also show that, for a univalent analytic self-map $\unicode[STIX]{x1D711}$ of $\mathbb{D}$, if $\unicode[STIX]{x1D711}$ has an angular derivative at some point of $\unicode[STIX]{x2202}\mathbb{D}$, then the essential norm of $C_{\unicode[STIX]{x1D711}}$ on the Dirichlet space is equal to one.

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.

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