Abstract
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.
Highlights
X − y n−μ f ( y) dy, The commutators of the fractional integral is defined by
We need the further assumption for Ω ( x, z)
We can find that when Ω ≡ 1 MΩ, μ is just the fractional maximal operator
Summary
X − y n−μ f ( y) dy, The commutators of the fractional integral is defined by. When μ ≡ 1 , the above integral takes the Cauchy principal value. The fractional integral operator with variable kernel TΩ,μ is defined by (2016) Boundedness of Fractional Integral with Variable Kernel and Their Commutators on Variable Exponent Herz Spaces. X − y n−μ f ( y) dy, The commutators of the fractional integral is defined by
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