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

Abstract

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 $m$th 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.