Higher Order Commutators of Fractional Integral Operator on the Homogeneous Herz Spaces with Variable Exponent

Abstract

By decomposing functions, we establish estimates for higher order commutators generated by fractional integral with BMO functions or the Lipschitz functions on the homogeneous Herz spaces with variable exponent. These estimates extend some known results in the literatures.

Grand Weighted Variable Herz-Morrey Spaces Estimates for Higher Order Commutators of Fractional Integrals

“…Since Kováčik and Rákosník developed the theory of variable exponent function spaces in [15], the variable exponent Lebesgue spaces L p(•) (R n ) have been extensively investigated, see [4,7,18]. Izuki introduced the variable exponent Herz spaces Kα,q p(•) (R n ), and considered the boundedness of commutators of fractional integrals in this spaces in [8], more research on the boundedness of operators in the above spaces see [9,22,23]. Subsequently, Izuki introduced the variable exponent Herz-Morrey spaces M Kα,λ q,p(•) (R n ) in [12], which is a generalized space of the Herz-Morrey spaces M Kα,λ q,p (R n ) in [16].…”

Higher order commutators of fractional integrals on Morrey type spaces with variable exponents

“…Recently, Wang, Fu and Liu made a further step and established the BMO and Lipschitz estimates for the higher order commutators on the Lebesgue spaces with variable exponent. We refer to for futher contributions in the study of these commutators in variable exponent spaces.…”