Marcinkiewicz Integral Operator Commutators Several Boundedness Results

In this thesis. some basic knowledge of weighted Hp(0<p<1) spaces are introduced. Using the methods of real harmonic analysis, also by the decom-positons of function spaces and the properties of weighted functions, we obtain the weighted boundedness of Marcinkiewicz integral operators is bounded from Hp(Rn) to Hp(Rn)(0<p<1), and discuss the commutators generated by BMO founctions and Marcinkiewicz integral with the kernel satisfying the logarith-mic type Lipschitz conditions is bounded from H1(Rn) to L1(Rn). Then, the definitions and atomic decompositions of Herz-Hardy spaces are introduced, by the results of boundedness of operators on LP, and the inequality estimates, we obtain above the commutator of Marcinkiewicz integral operators is bounded from HKα,pq,p to Kα,pq,b.