scholarly journals Boundedness of Fractional Oscillatory Integral Operators and Their Commutators in Vanishing Generalized Weighted Morrey Spaces

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Bilal Çekiç ◽  
Ayşegül Çelik Alabalık
Keyword(s):  
Integral Operators ◽  
Oscillatory Integral ◽  
Morrey Spaces ◽  
Integral Inequalities ◽  
Weighted Morrey Spaces ◽  
Oscillatory Integral Operators ◽  
Type Integral

In this article, we give the boundedness conditions in terms of Zygmund-type integral inequalities for oscillatory integral operators and fractional oscillatory integral operators on the vanishing generalized weighted Morrey spaces. Moreover, we investigate corresponding commutators.

scholarly journals Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 1023-1038
Author(s):  
Ali Akbulut ◽  
Amil Hasanov
Keyword(s):  
Fractional Integral ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Higher Order ◽  
Integral Inequalities ◽  
Rough Kernels ◽  
Weighted Morrey Spaces ◽  
Type Integral

AbstractIn this paper, we study the boundedness of fractional multilinear integral operators with rough kernels $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces Mp,ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with w ∈ Ap,q which ensures the boundedness of the operators $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ from ${M_{p,{\varphi _1}}}\left( {{w^p}} \right)\,{\rm{to}}\,{M_{p,{\varphi _2}}}\left( {{w^q}} \right)$ for 1 < p < q < ∞. In all cases the conditions for the boundedness of the operator $T_{\Omega ,\alpha }^{{A_1},{A_2}, \ldots ,{A_k}},$ are given in terms of Zygmund-type integral inequalities on (ϕ1, ϕ2) and w, which do not assume any assumption on monotonicity of ϕ1 (x,r), ϕ2(x, r) in r.

scholarly journals Boundedness of Oscillatory Integrals with Variable Calderón-Zygmund Kernel on Weighted Morrey Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yali Pan ◽  
Changwen Li ◽  
Xinsong Wang
Keyword(s):  
Harmonic Analysis ◽  
Singular Integrals ◽  
Integral Operators ◽  
Oscillatory Integral ◽  
Morrey Spaces ◽  
Oscillatory Integrals ◽  
Weighted Morrey Spaces ◽  
Oscillatory Integral Operators ◽  
Oscillatory Singular Integrals

Oscillatory integral operators play a key role in harmonic analysis. In this paper, the authors investigate the boundedness of the oscillatory singular integrals with variable Calderón-Zygmund kernel on the weighted Morrey spacesLp,k(ω). Meanwhile, the corresponding results for the oscillatory singular integrals with standard Calderón-Zygmund kernel are established.

scholarly journals Multilinear Commutators of Calderón-Zygmund Operator on Generalized Weighted Morrey Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Farida Ch. Alizadeh
Keyword(s):  
Weight Function ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Integral Inequalities ◽  
Zygmund Operator ◽  
Weighted Morrey Spaces ◽  
Type Integral ◽  
Multilinear Commutators

The boundedness of multilinear commutators of Calderón-Zygmund operatorTb→on generalized weighted Morrey spacesMp,φ(w)with the weight functionwbelonging to Muckenhoupt's classApis studied. When1<p<∞andb→=(b1,…,bm),bi∈BMO,i=1,…,m, the sufficient conditions on the pair(φ1,φ2)which ensure the boundedness of the operatorTb→fromMp,φ1(w)toMp,φ2(w)are found. In all cases the conditions for the boundedness ofTb→are given in terms of Zygmund-type integral inequalities on(φ1,φ2), which do not assume any assumption on monotonicity ofφ1(x,r),  φ2(x,r)inr.

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.

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