Some Properties of Generalized Orlicz Spaces
|School||Harbin University of Science and Technology|
|Keywords||Endpoint k- Endpoint k- strong endpoint λ- nature Consistent λ- nature|
According to various theories and application needs , Orlicz space for a variety of different forms of promotion, Fu p-Amemiya norm Orlicz spaces are Orlicz spaces promotion , denoted by L M, p space . k- endpoint , k- strong endpoint , λ- λ- consistent nature and nature is important Orlicz space geometric concepts , it k- strict convexity, midpoint Locally k- uniform convexity , endpoints, and has strict convexity close contact paper studies L M, p on the k- space endpoints , k- strong endpoint , λ- λ- nature and consistent nature thesis is divided into the following sections . Firstly , L M, p k- space and k- endpoint characterization of strict convexity problem is well known , endowed Luxemburg norm and the Orlicz norm Orlicz spaces k- endpoint is the point of an important class of state properties . p- Amemiya norm is the Luxemburg norm and the Orlicz norm of promotion, this section we present the L M, p space unit sphere that is necessary and sufficient k- endpoint criterion and accordingly get L M, p k- space is strictly convex and sufficient conditions . Secondly , L M, p space k- strong endpoint and midpoint locally uniformly convex k- characterization of the problem . endowed Luxemburg norm and the Orlicz norm Orlicz Spaces k- strong endpoint and midpoint locally uniformly convex k- equivalent characterization has proven that this section we present the L M, p < / sub> space unit sphere point is k- strong and sufficient conditions endpoint , which introduced the L M, p midpoint Locally k- space is a necessary and sufficient condition uniformly convex Finally , L M, p space and consistent nature of λ- λ- nature endowed Luxemburg norm and the Orlicz norm Orlicz spaces and consistent nature of λ- λ- nature , many scholars have done a thorough research , and got a lot of good results in this section, we have come to L M, p space with λ- nature , and gives the L M, p space nature has a consistent λ- sufficient and necessary conditions .