Geometric properties of Orlicz spaces equipped with p-Amemiya norms : results and open questions

• Autorzy: Wisła M.

Identyfikatory

DOI

0.14708/cm.v55i2.1132

• Języki publikacji: EN

Abstrakty

EN

The classical Orlicz and Luxemburg norms generated by an Orlicz function Φ 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∥_Φ,p=inf_k>011/k(1+IpΦ(kx))^1/p, where 1≤p≤∞ (under the convention: (1+u∞)1/∞=limp→∞(1+up)1/p=max1,u for all u≥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.

Słowa kluczowe

EN

rotundity; non-squareness; uniform monotonicity; dominated best approximation problem; Amemiya type norm

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2015
• Tom: Vol 55, No. 2
• Strony: 183--209
• Opis fizyczny: Bibliogr.49 poz., wykr.

Twórcy

autor

Wisła M.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland

Bibliografia

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