- Tytuł:
- Geometric properties of Orlicz spaces equipped with \(p\)-Amemiya norms − results and open questions
- Autorzy:
- Wisła, Marek
- Powiązania:
- https://bibliotekanauki.pl/articles/746287.pdf
- Data publikacji:
- 2015
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
rotundity
non-squareness
uniform monotonicity
dominated best approximation problem
Amemiya type norm - Opis:
- The classical Orlicz and Luxemburg norms generated by an Orlicz function \(\Phi\) can be defined with the use of the Amemiya formula [H. Hudzik and L. Maligranda, Amemiya norm equals Orlicz norm in general, Indag. Math. 11 (2000), no. 4, 573-585]. Moreover, in this article Hudzik and Maligranda suggested investigating a family of p-Amemiya norms defined by the formula \(\|x\|_{\Phi,p}=\inf_{k>0} \frac{1}{k} (1+I_\Phi^p(kx))^{1/p}\), where \(1\le p\le\infty\) (under the convention: \((1+u^\infty)^{1/\infty}=\lim_{p\to\infty}(1+u^p)^{1/p}=\max{1,u}\) for all \(u\ge 0\)). Based on this idea, a number of papers have been published in the past few years. In this paper, we present some major results concerning the geometric properties of Orlicz spaces equipped with p-Amemiya norms. In the last section, a more general case of Amemiya type norms is investigated. A few open questions concerning this theory will be stated as well.
- Źródło:
-
Commentationes Mathematicae; 2015, 55, 2
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł