On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces

AbstractLet TΩ be the singular integral operator with kernel , where Ω is homogeneous of degree zero, has mean value zero, and belongs to Lq(Sn–1) for some q ∊ (1,∞). In this paper, the authors establish the compactness on weighted Lp spaces and the Morrey spaces, for the commutator generated by CMO(ℝn) function and TΩ. The associated maximal operator and the discrete maximal operator are also considered.

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

Open Mathematics ◽

10.1515/math-2020-0033 ◽

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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Boundedness of a Class of Oscillatory Singular Integral Operators and Their Commutators with Rough Kernel on Weighted Central Morrey Spaces

Mathematics ◽

10.3390/math8091455 ◽

2020 ◽

Vol 8 (9) ◽

pp. 1455

Author(s):

Yongliang Zhou ◽

Dunyan Yan ◽

Mingquan Wei

Keyword(s):

Singular Integral ◽

Integral Operators ◽

Morrey Spaces ◽

Rough Kernel ◽

Singular Integral Operators ◽

Oscillatory Singular Integral

In this paper, we establish the boundedness of a class of oscillatory singular integral operators with rough kernel on central Morrey spaces. Moreover, the boundedness for each of their commutators on weighted central Morrey spaces was also obtained. We generalized some existing results.

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Singular Integral Operators, Morrey Spaces and Fine Regularity of Solutions to PDE's

Potential Analysis ◽

10.1023/b:pota.0000010664.71807.f6 ◽

2004 ◽

Vol 20 (3) ◽

pp. 237-263 ◽

Cited By ~ 45

Author(s):

Dian K. Palagachev ◽

Lubomira G. Softova

Keyword(s):

Singular Integral ◽

Integral Operators ◽

Morrey Spaces ◽

Singular Integral Operators ◽

Regularity Of Solutions

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Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

Abstract and Applied Analysis ◽

10.1155/2008/237937 ◽

2008 ◽

Vol 2008 ◽

pp. 1-21 ◽

Cited By ~ 7

Author(s):

Guoen Hu ◽

Haibo Lin ◽

Dachun Yang

Keyword(s):

Singular Integral ◽

Maximal Operator ◽

Weak Type ◽

Integral Operators ◽

Singular Integral Operators ◽

Maximal Operators ◽

Homogeneous Type ◽

Spaces Of Homogeneous Type ◽

Littlewood Maximal Operator

WeightedLpforp∈(1,∞)and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.

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