一类次线性算子在齐型空间上的加权有界性

Weighted Boundedness of Some Sublinear Operators on Homogeneous Type Spaces

设X是齐型空间,φ是Young函数,设次线性算子T是从Lφ(X,ω)到Lφ(X+,β)有界的,本文建立了T从Morrey空间Lφ,λ(X,ω)到Lφ,λ(X+,β)的加权有界性.特别地建立了HardyLittlewood极大算子.

Let X be Homegeneous type space,φ is a Young function. Suppose that sublinear operator T is boundedness from L~φ(X,ω) to L~φ(X^+,β). Then, it is proved that T is weighted boundedness from Morrey spaces L~ φ,λ(X,ω) to L~ φ,λ(X^+,β). Specielly, the boundedness of Hardy-Littlewood maximal opertor is proved.