scholarly journals A note on fractional integral operators on Herz spaces with variable exponent

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Meng Qu ◽  
Jie Wang
Keyword(s):  
Variable Exponent ◽  
Fractional Integral ◽  
Integral Operators ◽  
Herz Spaces ◽  
Fractional Integral Operators

scholarly journals Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Xukui Shao ◽  
Shuangping Tao
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Variable Kernel ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Weak Morrey Spaces

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.

scholarly journals Estimates of Fractional Integral Operators on Variable Exponent Lebesgue Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Canqin Tang ◽  
Qing Wu ◽  
Jingshi Xu
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Type Inequality ◽  
Integral Operators ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Variable Exponent Lebesgue Spaces

By some estimates for the variable fractional maximal operator, the authors prove that the fractional integral operator is bounded and satisfies the weak-type inequality on variable exponent Lebesgue spaces.

scholarly journals Fractional integral operators on Herz spaces for supercritical indices

2011 ◽  
Vol 9 (2) ◽  
pp. 179-190 ◽  
Author(s):  
Yasuo Komori-Furuya
Keyword(s):  
Function Space ◽  
Fractional Integral ◽  
Integral Operators ◽  
Lipschitz Space ◽  
Herz Spaces ◽  
Fractional Integral Operators

We consider the boundedness of fractional integral operatorsIβon Herz spacesKqα,p(Rn), whereq≥n/β. We introduce a new function space that is a variant of Lipschitz space. Our results are optimal.

scholarly journals Multilinear fractional integral operators on central Morrey spaces with variable exponent

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongbin Wang ◽  
Jingshi Xu
Keyword(s):  
Variable Exponent ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operators ◽  
Multilinear Fractional Integral

AbstractIn this paper, we obtain the boundedness of the multilinear fractional integral operators and their commutators on central Morrey spaces with variable exponent.

Two-weight norm estimates for sublinear integral operators in variable exponent Lebesgue spaces

2014 ◽  
Vol 51 (3) ◽  
pp. 384-406 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Measure Space ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Integral Operators ◽  
Doubling Condition ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Norm Estimates ◽  
Variable Exponent Lebesgue Spaces ◽  
Necessary And Sufficient

Two-weight norm estimates for sublinear integral operators involving Hardy-Littlewood maximal, Calderón-Zygmund and fractional integral operators in variable exponent Lebesgue spaces are derived. Operators and the space are defined on a quasi-metric measure space with doubling condition. The derived conditions are written in terms ofLp(·)norms and are simultaneously necessary and sufficient for appropriate inequalities for maximal and fractional integral operators mainly in the case when weights are of radial type.

scholarly journals Boundedness of several operators on weighted Herz spaces

2009 ◽  
Vol 7 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Yasuo Komori ◽  
Katsuo Matsuoka
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Herz Space ◽  
Herz Spaces ◽  
Fractional Integral Operators

We consider the boundedness of singular integral operators and fractional integral operators on weighted Herz spaces. For this purpose we introduce generalized Herz space. Our results are the best possible.

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