Weighted Inequalities For Fractional And Commutators Of Fractional Maximal Integral Operators With Rough Kernels

Riesz potential is an important operator in harmonic analysis,and fractionalintegral with a homogeneous kernel or a rough kernel is a lively field arising fromresearches on Riesz potential.Recent years have seen rich achievements about theboundedness of the fractional integral with a homogeneous(rough) kernel in di?erentspaces.In this paper, we mainly study conditions which are sufficient for weightedinequalities for fractional and commutators of fractional maximal integral operatorswith rough kernels.In ChapterⅠ, we briefly introduce the summary of the fractional intergral andcommutators generated by fractional integral operators,overview the bounddeness offractional integral operators with rough kernels on Hardy spaces and give a researchsummary of the studies at home and abroad.In ChapterⅡ, we mostly give sufficient conditions for two-weight weak-typenorm inequalities for fractional integral operators with rough kernel, which is acertain A_p-type condition relevant to Orlicz function the weights (u,v) should besatisfied.In ChapterⅢ, we chiefly give sufficient conditions for the weighted bounded-ness of commutators generated by fractional maximal operators with rough kernelsand BMO functions by applying Stein–Weiss operator interpolation theorems forvariable measures.