The Research Of Operator Theory In Generalized Orlicz Spaces On The Unit Disk

Generalized Orlicz space L^?(·)is relatively general space class,which includes the classical Lebesgue spaces,Orlicz spaces,and variable Lebesgue spaces as so on.Recently,generalized Orlicz space has attracted lots of attentions and studies since the generality and richness of its theory.In this thesis,we research some problems related to operator theory on the generalized Orlicz spaces defined on the unit disk.Maximal operator on the generalized Orlicz spaces of the unit disk is researched firstly.Maximal operator is a class of important operator on function spaces,and has closely relation with Carleson measure,imbedding operator and projection operator.The boundedness of the maximal operator on the generalized Orlicz spaces of the unit disk is proved,and an estimation for its norm is obained.Then,a version of the Rubio de Francia extrapolation theorem on generalized Or-licz spaces of the unit disc is researched.By discussion of the Bekoll?e-Bonami weights and construction of Rubio de Francia iteration operator based on maximal operators,an inequality in terms of Bekoll?e-Bonami weights is obtained.As an application,the boundedness of Bergman projection on weighted Bergman-Orlicz spaces is discussed.The isomorphism relation between dual space and associated space on Bergman-Orlicz space is considered.