The Continuity For Maximal Operator Of Bochner-Riesz And Its Commutators

In 2002,Tang Canqin and Yang Dachun gave the definition of generalized fractional integral and showed that the classical fractional integral only is its speacial case.After this,people greatly devoted into the study of the generalized fractional integral and its commutator,obtained many vauled results.In chapter 1,we will discuss the boundedness of the high orders of generalized fractional integral.Yuang Mingrong and Xue Qingyin proved the boundedness of the Marcinkiewicz integral in generalized Campanato space in 2002(see[9]).Motivated by this,we will prove the boundedness of the classical singular integral in generalized Campanato space in the chapter 2.The papers[21][27] discussed the character of the Campanato and Morrey space; Jiang Yinsheng proved the boundedness of the commutator of maximal Bochner-Riesz operator in Hardy space,and We know the classical Morrey space is the dual of the Hardy space .Further,we proved the boundedness of the maximal Bochner-Riesz operator and its commutator in the generalized Morrey space in the chapter 3.We know Lebesgue space and Hardy space are the speacial case of the homogeneous Trible-Lizorkin space,But,this is not right for the weak Hardy space and the weak Lebesgue space .So,by the papers[15][17],we proved the boundedness of the maximal Bochner-Riesz operator in the weak Hardy space and its commutator in Herz type Hardy space in chapter4.