The Boundedness Of The Commutator Of Fractional Maximal Function In Variable Exponential Space

Bying using the properties of BMO functions,Lipschitz functions,the estimates of the classical inequalities and the properties of variable exponent,we proved the equivalent characterization for the boundedness of the commutators generated by fractional maxi-mal operators and BMO functions on Morrey spaces with variable exponent.Based on the definition of the Herz-Morrey spaces with variable exponent,the boundedness of the commutators generated by fractional maximal operators and BMO functions on variable exponent Herz-Morrey spaces was established.We discussed the boundedness of the com-mutators generated by fractional maximal operators and Lipschitz functions from MKq1,p1(·)?,?to MKq2,p2(·)?,?.By the boundedness of the multilinear commutators generated by fraction-al maximal operators and Lipschitz functions on Lp,the boundedness of the multilinear fractional maximal commutators on the homogeneous Herz-Morrey spaces with variable exponents is obtained.