Boundedness Of Marcinkiewicz Integral On Some Kinds Of Spaces

The research of the boundedness of the operators is one of the important topicsin harmonic analysis.In this dissertation, the boundedness for Marcinkiewicz integraloperators and its commutators on some kinds of spaces are considered.The first chapter discusses that when satisfying two types Dini conditions,thebounedeness of the operatorμ,b with variable kernel from the Herz-type Hardyspaces to Herz-type spaces, where b∈Lipβ.The second chapter studies the continuity of the higher order commutatorsμm,b,generated by Marcinkiewicz integralμm with variable kernel and a BMO functionb(x).The third chapter discusses the behavior on BLO spaces for the higher-dimensionalparameterized Marcinkiewicz integral operator, prove that [μρ(f)]2 is either infiniteeverywhere or finite almost everywhere.