Weighted boundedness for multilinear singular integral operators with non-smooth kernels on Morrey spaces

2010 ◽  
Vol 104 (1) ◽  
pp. 115-127 ◽  
Author(s):  
Zhou Xiaosha ◽  
Liu Lanzhe
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Multilinear Singular Integral ◽  
Smooth Kernels

scholarly journals Multilinear Singular Integral Operators on Generalized Weighted Morrey Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yue Hu ◽  
Zhang Li ◽  
Yueshan Wang
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Zygmund Operator ◽  
Multilinear Singular Integral ◽  
Weighted Morrey Spaces

The purpose of this paper is to discuss the boundedness properties of multilinear Calderón-Zygmund operator and its commutator on the generalized weighted Morrey spaces.

Weighted boundedness of multilinear singular integral operators with non-smooth kernels for the extreme cases

2020 ◽  
Vol 27 (2) ◽  
pp. 271-284
Author(s):  
Weiping Kuang
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Multilinear Operators ◽  
Multilinear Singular Integral ◽  
Smooth Kernels

AbstractThe weighted boundedness properties of multilinear operators associated to singular integral operators with non-smooth kernels for extreme cases are obtained.

scholarly journals B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials on B-Morrey spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 715-730
Author(s):  
Javanshir J. Hasanov ◽  
Rabil Ayazoglu ◽  
Simten Bayrakci
Keyword(s):  
Differential Operator ◽  
Singular Integral ◽  
Riesz Potential ◽  
Type Theorem ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Sobolev Type ◽  
Riesz Potentials ◽  
Bessel Differential Operator

Abstract In this article, we consider the Laplace-Bessel differential operator {\Delta }_{{B}_{k,n}}=\mathop{\sum }\limits_{i=1}^{k}\left(\frac{{\partial }^{2}}{\partial {x}_{i}^{2}}+\frac{{\gamma }_{i}}{{x}_{i}}\frac{\partial }{\partial {x}_{i}}\right)+\mathop{\sum }\limits_{i=k+1}^{n}\frac{{\partial }^{2}}{\partial {x}_{i}^{2}},{\gamma }_{1}\gt 0,\ldots ,{\gamma }_{k}\gt 0. Furthermore, we define B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials associated with the Laplace-Bessel differential operator. Moreover, we also obtain the boundedness of the B-maximal commutator {M}_{b,\gamma } and the commutator {[}b,{A}_{\gamma }] of the B-singular integral operator and Hardy-Littlewood-Sobolev-type theorem for the commutator {[}b,{I}_{\alpha ,\gamma }] of the B-Riesz potential on B-Morrey spaces {L}_{p,\lambda ,\gamma } , when b\in {\text{BMO}}_{\gamma } .

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