Uniform rotundity in every direction of Orlicz-Sobolev spaces

Abstract

Abstract In this paper, we study the extreme points and rotundity of Orlicz-Sobolev spaces. Analyzing and combining the properties of both Orlicz spaces and Sobolev spaces, we get the sufficient and necessary criteria for Orlicz-Sobolev spaces equipped with a modular norm to be uniformly rotund in every direction.

Keywords

• Orlicz-Sobolev spaces
• rotund
• modular norm