Sector Results In Several Morrey, Herz Spaces In The Non-doubling Measures

Letμbe a non-doubling measure.The only condition thatμmust satisfy is the growth condition.In this thesis,we define a class of commutators[b,T] and[b,T_γ]which are generated by Calder(?)n-Zygmund operator and fractional integral operator with RBMO(μ) function b for the non-doubling measure respectively. By the method of Soria,using the Morrey-Herz space with the characterization of Herz space and the properties of the RBMO functions enjoying with the classical BMO,and the properties of K_Q,R for any two cubes on non-doubling measure,first,we show the boundedness of the Hardy-Littlewood fractional maximal commutator M_b^d on Morrey-Herz space with non-doubling measure,then obtain the boundedness of[b,T]and[b,T_b^γ]on Morrey-Herz space. Besides,the boundedness of Marcinkiewicz integral M for non-doubling measure on Morrey-Herz space is also discussed and the similar result is obtained.