L2L^{2} boundedness for commutators of fractional differential type Marcinkiewicz integral with rough variable kernel and BMO Sobolev spaces

2020 ◽  
Vol 27 (4) ◽  
pp. 529-540
Author(s):  
Yanping Chen ◽  
Yong Ding ◽  
Kai Zhu
Keyword(s):  
Sobolev Spaces ◽  
Marcinkiewicz Integral ◽  
Variable Kernel ◽  
Differential Type ◽  
Fractional Differential ◽  
Rough Variable Kernel

AbstractIn this paper, for {0<\gamma<1} and {b\in I_{\gamma}(\mathrm{BMO})}, the authors give the {L^{2}({\mathbb{R}}^{n})} boundedness of {\mu_{\gamma;b}}, the commutator of a fractional differential type Marcinkiewicz integral with rough variable kernel, which is an extension of some known results.

Commutators of Marcinkiewicz integral with rough kernels on Sobolev spaces

2011 ◽  
Vol 27 (7) ◽  
pp. 1345-1366
Author(s):  
Yan Ping Chen ◽  
Yong Ding ◽  
Xin Xia Wang
Keyword(s):  
Sobolev Spaces ◽  
Marcinkiewicz Integral ◽  
Rough Kernels

scholarly journals The boundedness of Marcinkiewicz integral with variable kernel

2009 ◽  
Vol 53 (1) ◽  
pp. 197-217 ◽  
Author(s):  
Chin-Cheng Lin ◽  
Ying-Chieh Lin ◽  
Xiangxing Tao ◽  
Xiao Yu
Keyword(s):  
Marcinkiewicz Integral ◽  
Variable Kernel

scholarly journals Solutions of Fractional Differential Type Equations by Fixed Point Techniques for Multivalued Contractions

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hasanen A. Hammad ◽  
Hassen Aydi ◽  
Manuel De la Sen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Differential Type ◽  
Fractional Differential ◽  
Multivalued Contractions

This paper involves extended b − metric versions of a fractional differential equation, a system of fractional differential equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting of an extended b − metric space. Thereafter, by making consequent use of the fixed point technique, short and simple proofs are obtained for solutions of a fractional differential equation, a system of fractional differential equations and a two-dimensional linear Fredholm integral equation.

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