In this paper, we study the boundedness of the fractional integral with variable kernel. Under some assumptions, we prove that such kind of operators is bounded from the variable exponent Herz-Morrey spaces to the variable exponent Herz-Morrey spaces.
In this paper, we study the boundedness of the fractional integral operator and their commutator on Herz spaecs with two variable exponents ( ) ( ) p q , ⋅ ⋅ . 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.
In this paper, we obtain the boundedness of commutators generated by the Calderón-Zygmund operator, BMO functions and Lipschitz function on Herz-Morrey-Hardy spaces with variable exponent HMK α(•),q p(•),λ (R n ).
The aim of this paper is to study the boundedness of Calderón-Zygmund operator and their commutator on Herz Spaces with two variable exponents ( ) ( ) . , . p q . By applying the properties of the Lebesgue spaces with variable exponent, the boundedness of the Calderón-Zygmund operator and the commutator generated by BMO function and Calderón-Zygmund operator is obtained on Herz space.
By using the boundedness results for the commutators of the fractional integral with variable kernel on variable Lebesgue spaces L p(•) (R n ), the boundedness results are established on variable exponent Herz−Morrey spaces MK α,λ q,p(•) (R n ).
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