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

摘要

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 ndimensional fractional Hardy operators and bounded mean oscillation (BMO) function are also considered.We note that, even in the special case ofm=1, the obtained results are also new.