On n-dimensional fractional Hardy operators and commutators in variable Herz-type spaces

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Based on the theory of variable exponents and atomic decomposition, we study the boundedness of n-dimensional fractional Hardy operators on variable Herz and Herz-type Hardy spaces, where the three main indices are variable exponents. The corresponding boundedness for the mth order commutators generated by the n-dimensional fractional Hardy operators and bounded mean oscillation (BMO) function are also considered. We note that, even in the special case of m=1, the obtained results are also new.