rough kernel
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Author(s):  
Feri̇t Gürbüz

In this paper, applying some properties of rough kernel and using some technical lemmas, we prove various norm inequalities concerning Marcinkiewicz integral with rough kernel. Indeed, we extend some known results on singular integrals to Marcinkiewicz integrals.



Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long

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.



Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1455
Author(s):  
Yongliang Zhou ◽  
Dunyan Yan ◽  
Mingquan Wei

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.



2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Lei Zhang ◽  
Shaoguang Shi

This paper is devoted in characterizing the central BMO ℝn space via the commutator of the fractional Hardy operator with rough kernel. Precisely, by a more explicit decomposition of the operator and the kernel function, we will show that if the symbol function belongs to the central BMO ℝn space, then the commutator are bounded on Lebesgue space. Conversely, the boundedness of the commutator implies that the symbol function belongs to the central BMO ℝn space by exploiting the center symmetry of the Hardy operator deeply.



2020 ◽  
Vol 96 (3-4) ◽  
pp. 377-399
Author(s):  
Xiangxing Tao ◽  
Guoen Hu


Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1147-1156
Author(s):  
Ferit Gürbüz

In this paper, the author introduces parabolic generalized local Morrey spaces and parabolic local Campanato spaces, respectively and also establishes parabolic local Campanato estimates for commutators of parabolic fractional maximal and integral operators with rough kernel on parabolic generalized local Morrey spaces.



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