Boundedness Of Operators On Herz Spaces Of The Homogeneous Spaces

In this dissertation,some boundedness of operators on Herz spaces of homogeneous spaces are established.A triple(X,d,μ)is called a space of homogeneous type,if X is a non-empty set,and d is a quasi-metric on X,along with a non-negative measureμsatisfyingμ(B(x,2r))(?)Aμ,(B(x,r))＜∞for any x∈X,r∈[0,∞),where B(x,r)= {y∈X|d(x,y)＜r},and A denotes a constant independent of r and x.In the first chapter,we will discuss the boundedness of fractional maximal operators M_αof Herz spaces on the homogeneous spaces,in the course of proof we use the decomposition characterization of these spaces.In the second chapter,we will discuss the boundedness of maxi-mal operator M and fractional maximal operators M_αof weighted Herz spaces on the homogeneous spaces.In the last chapter,we will discuss the boundedness of the commu-tator of the maximal operator.