WEIGHTED LOCAL MORREY SPACES

摘要

We discuss the boundedness of linear and sublinear operatorsin two types of weighted local Morrey spaces.One isdefined byNatasha Samko in 2008.The other is defined by Yasuo Komori-Furuya and Satoru Shirai in 2009.We characterize the class of weightsfor which the Hardy-Littlewood maximal operatoris bounded.Under a certain integral condition it turns out thatthe singular integral operatorsare bounded if and only if the Hardy-Littlewood maximal operatoris bounded.As an application of the characterization,the power weight function || is considered.The condition on for which the Hardy-Littlewood maximal operatoris bounded can be described completely.