Some Properties Of ?-pseudo Almost Periodic Functions On Measure Spaces

In this paper,we study the properties of ?-pseudo almost periodic function,?-pseudo almost periodic function including almost periodic function,asymptotic almost periodic function,pseudo almost periodic function,weighted pseudo almost periodic function and so on.On the one hand,some classical results can be further studied by learning the properties of this kind of function,on the other hand,the commonality of all the above function classes can be studied from a unifying point of view.In the previous,some researchers have done a series of studies on the properties of ?-pseudo almost periodic functions,now we did a little bit more research,more specifically in the following aspects:Firstly,because of the convolution invariance is important in some applications of ?-pseudo almost periodic functions,we investigate the convolution operator K defined on the space PAP(X,?),and establish two sufficient conditions for the convolution invariant of the ?-ergodic space,then the relative results of the invariance of PAP(X,?)convolution are obtained.Secondly,we consider when their corresponding ?-ergodic spaces equal for two non-equivalent measures ?1 and ?2.Finally,we study the relationship between ?-ergodic zero set and C0(X),on this basis,we discuss the relationship between the ?-pseudo almost periodic function and the asymptotic almost periodic function.