Author(s)

Afif Abdalmonem^1,2, Omer Abdalrhman^1,3, Shuangping Tao^1*

¹College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China.
²Faculty of Science, University of Dalanj, Dalanj, Sudan.
³College of Education, Shendi University, Shendi, Sudan.

In this paper, we study the boundedness of the fractional integral operator and their commutator on Herz spaecs with two variable exponents . By using the properties of the variable exponents Lebesgue spaces, the boundedness of the fractional integral operator and their commutator generated by Lipschitz function is obtained on those Herz spaces.

Fractional Integral, Variable Kernel, Commutator, Variable Exponent, Lipschitz Space, Herz Spaces

Abdalmonem, A. , Abdalrhman, O. and Tao, S. (2016) Boundedness of Fractional Integral with Variable Kernel and Their Commutators on Variable Exponent Herz Spaces. Applied Mathematics, 7, 1165-1182. doi: 10.4236/am.2016.710104.