Various characterizations are given of the exponential Orlicz space L exp t r and the Orlicz -Lorentz space L exp t r , t r . By way of application we give a simple proof of the celebrated theorem of BrΓ©zis and Wainger concerning a limiting case of a Sobolev imbedding theorem.
On Smallest and Largest Orlicz Spaces
β Scribed by Henryk Hudzik
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 289 KB
- Volume
- 141
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
There are found the smallest and largest spaces among a11 ORLICZ spaces generated by non-decreasing ORLICZ functions and also among all ORLICZ spaces generated by 8-convex OBLICZ functions, 0 < 8 S 1.
π SIMILAR VOLUMES
## Abstract Spaces of Lorentz type called OrliczβLorentz spaces are studied. There are given necessary and sufficient conditions for the spaces to be order continuous, separable, __KB__βspaces and to contain isometric or isomorphic copy of __l__β or __c__~0~. Moreover a criterion for strict convexi
## Abstract We introduce the notions of __X__~d,s(x),Ο~βlinear multifunctional and __X__~d,s(x),Ο~βlinear continuous multifunctional. We generalize the theorems on linear bounded functionals in the MusielakβOrlicz space.
The aim of this note is to study the IP-complemented subspaces in ORLICZ function spaces LV(0, co) over the infinite interval (0, co). Several results previously given by the authors in ([H-R,]) for the ORLICZ spaces 1, and Lq [O, 11 are extended to the class of ORLICZ function spaces Lv(O, 00). Th
On the unit ball of an Orlicz function space the denting points, weak U denting points, and quasi-denting points coincide. But on the unit ball of an Orlicz sequence space the quasi-denting points are different from the denting points and weak U denting points. We also show that the weak U drop prop