Poincaré Inequality With Local Weights Under Nondoubling Measures

This paper studies the local weighted Poincaré inequality of under nondoubling measures.First,this paper introduces the different expressions of Poincaré inequality and the new achievements of current researches.Secondly,the local weighted weak BMO-Poincaré inequality under nondoubling measures is obtained in terms of Besicovitch-Calderon-Zygimxnd decomposition and weighted Ds condition,by which the the local weighted strong type BMO-Poincaré inequality as well as Poincaré inequality under nondoubling measures axe proved to be valid.This paper gave a new Poincaré inequality,which enriches the related conclu-sions of Poincaré inequality and deepens scholars’ understanding of the Poincaré inequality.