Uniform convexity and associate spaces

Czechoslovak Mathematical Journal

Petteri Harjulehto, Peter Hästö¹ 

关键词: generalized Orlicz space;    Musielak-Orlicz space;    nonstandard growth;    variable exponent;    double phase;    uniform convexity;    associate space;   

DOI  :  10.21136/CMJ.2018.0054-17

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  We prove that the associate space of a generalized Orlicz space $L^{\phi(\cdot)}$ is given by the conjugate modular $\phi^*$ even without the assumption that simple functions belong to the space. Second, we show that every weakly doubling $\Phi$-function is equivalent to a doubling $\Phi$-function. As a consequence, we conclude that $L^{\phi(\cdot)}$ is uniformly convex if $\phi$ and $\phi^*$ are weakly doubling.

【 授权许可】

Unknown