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.
Highlights
Let b be a locally integrable function, 0 < β < n, and m ∈ N; the higher order commutators of fractional integral operator Iβm,b are defined by Iβm,bf (x) = ∫Rn [b (x) − b (y)]m x − yn−β f (y) dy. (1)Obviously, Iβ0,b = Iβ and Iβ1,b = [b, Iβ]
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
The famous Hardy-Littlewood-Sobolev theorem tells us that the fractional integral operator Iβ is a bounded operator from the usual Lebesgue spaces Lp1 (Rn) to Lp2 (Rn) when 0 < p1 < p2 < ∞ and 1/p1 − 1/p2 = β/n
Summary
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.
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