Orlicz-Sobolev空间的Radon-Nikodym性质和围线长

RADON-NIKODYM PROPERTY AND GIRTH OF ORLICZ-SOBOLEV SPACES

Orlicz-Sobolev空间作为一种特殊的Banach空间 ,在非线性问题的研究中具有重要作用 .本文结合Orlicz空间和Sobolev空间的技巧得到分别赋Luxem burg范围和赋Orlicz范数的Orlicz-Sobolev空间具有Radon -Nikodym性质的充要条件 。

As a special Banach space, Orlicz-Sobolev space has played important roles in studying non-linear problems. This paper gives necessary and sufficient conditions for Radon-Nikodym property of Orlicz-Sobolev spaces with Luxemburg norm and Orlicz norm by combining the skill of Orlicz spaces with that of Sobolev spaces. Moreover, this paper estimates the girth of Orlicz-Sobolev spaces with Luxemburg norm.