Boundedness For Commutator Of Fractional Integral On Nonhomogeneous Space

Supposeμis a non-negative Radon measure on Euclidean space Rd which onlysatisfies the following growth condition: there exist constants C > 0 and n∈(0, d]such that for all x∈Rd and r > 0, where B(x, r) = {y∈Rd : |y?x| < r}, The space (Rd,μ) is called a nonhomogeneousspace.In this thesis, the boundedness for commutator generated by fractional integraloperator and RBMO(μ) function on nonhomogeneous space is considered.In the first chapter, applying the atomic block decomposition technique, weprove the commutator of fractional integral operator is bounded from Hb1 ,p(μ) intoLr(μ) .In the second chapter, we refer to the proof method in Herz-type space andestablish the boundedness for the commutator of fractional integral operator onMorrey-Herz space in non-homogeneous space.In the third chapter, we obtain the boundedness for the commutator of frac-tional integral operator on generalized Morrey space in non-homogeneous space, theconclusion in this part contains the corresponding result on Morrey space.