scholarly journals On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Sha He ◽  
Xiangxing Tao
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Multilinear Operators ◽  
Rough Kernels ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Maximal Singular Integral

We study some multilinear operators with rough kernels. For the multilinear fractional integral operatorsTΩ,αAand the multilinear fractional maximal integral operatorsMΩ,αA, we obtain their boundedness on weighted Morrey spaces with two weightsLp,κ(u,v)whenDγA∈Λ˙β  (|γ|=m-1)orDγA∈BMO  (|γ|=m-1). For the multilinear singular integral operatorsTΩAand the multilinear maximal singular integral operatorsMΩA, we show they are bounded on weighted Morrey spaces with two weightsLp,κ(u,v)ifDγA∈Λ˙β  (|γ|=m-1)and bounded on weighted Morrey spaces with one weightLp,κ(w)ifDγA∈BMO  (|γ|=m-1)form=1,2.

scholarly journals Weighted Endpoint Estimates for Commutators of Singular Integral Operators on Orlicz-Morrey Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Jinyun Qi ◽  
Hongxia Shi ◽  
Wenming Li
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Maximal Operators ◽  
Fractional Integral Operators

In this paper, we obtain the weighted endpoint estimates for the commutators of the singular integral operators with the BMO functions and the associated maximal operators on Orlicz-Morrey Spaces. We also get the similar results for the commutators of the fractional integral operators with the BMO functions and the associated maximal operators.

Characterizations of bounded mean oscillation through commutators of bilinear singular integral operators

2016 ◽  
Vol 146 (6) ◽  
pp. 1159-1166 ◽  
Author(s):  
Lucas Chaffee
Keyword(s):  
Singular Integral ◽  
Wide Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Bounded Mean Oscillation ◽  
Fractional Integral Operators ◽  
Pointwise Multiplication ◽  
Bilinear Operators ◽  
Mean Oscillation

We characterize bounded mean oscillation in terms of the boundedness of commutators of various bilinear singular integral operators with pointwise multiplication. In particular, we study commutators of a wide class of bilinear operators of convolution type, including bilinear Calderón–Zygmund operators and the bilinear fractional integral operators.

scholarly journals Multilinear Singular and Fractional Integral Operators on Weighted Morrey Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hua Wang ◽  
Wentan Yi
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Multiple Weights ◽  
Multilinear Fractional Integrals

We will study the boundedness properties of multilinear Calderón-Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.

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.

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