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.

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 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 Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

2014 ◽  
Vol 64 (2) ◽  
pp. 365-386 ◽  
Author(s):  
Vagif Sabir Guliyev ◽  
Turhan Karaman ◽  
Rza Chingiz Mustafayev ◽  
Ayhan Şerbetçi
Keyword(s):  
Morrey Spaces ◽  
Zygmund Operator ◽  
Weighted Morrey Spaces ◽  
Sublinear Operators

scholarly journals Toeplitz Type Operators Associated with Generalized Calderón-Zygmund Operator on Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Bijun Ren ◽  
Enbin Zhang
Keyword(s):  
Morrey Space ◽  
Morrey Spaces ◽  
Linear Operators ◽  
Identity Operator ◽  
Zygmund Operator ◽  
Weighted Bmo ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces ◽  
Bmo Spaces ◽  
Toeplitz Type Operator

LetT1be a generalized Calderón-Zygmund operator or±I(the identity operator), letT2andT4be the linear operators, and letT3=±I. Denote the Toeplitz type operator byTb=T1MbIαT2+T3IαMbT4, whereMbf=bfandIαis the fractional integral operator. In this paper, we investigate the boundedness of the operatorTbon weighted Morrey space whenbbelongs to the weighted BMO spaces.

scholarly journals On a relation to two basic Hilbert-type integral inequalities

2009 ◽  
Vol 40 (3) ◽  
pp. 217-223 ◽  
Author(s):  
Bicheng Yang
Keyword(s):  
Weight Function ◽  
Integral Inequality ◽  
Equivalent Form ◽  
Constant Factor ◽  
Integral Inequalities ◽  
Real Analysis ◽  
Best Constant ◽  
Type Integral ◽  
Best Constant Factor ◽  
Hilbert Type

In this paper, by using the way of weight function and the technic of real analysis, a new integral inequality with some parameters and a best constant factor is given, which is a relation to two basic Hilbert-type integral inequalities. The equivalent form and the reverse forms are considered.

Reverse Hardy-Type Integral Inequalities with Two Independent Parameters

2013 ◽  
Vol 811 ◽  
pp. 720-724
Author(s):  
Bei Yang ◽  
Guang Sheng Chen
Keyword(s):  
Weight Function ◽  
Integral Inequalities ◽  
Hardy Type ◽  
Type Integral ◽  
Independent Parameters

By introducing two independent parameters , using weight function and the method of real analisis,some extended reverse Hardy-type integral inequalities were established, and their constant factors were proved to be the optimum value. we have also considered the equivalent forms and some particular results.

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