Some Rotundities of Orlicz–Lorentz Spaces

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2024-03-15 DOI:10.1007/s10114-024-2551-1

Wan Zhong Gong, Peng Wang

引用次数: 0

Abstract

K-UR, K-LUR and K-R are the generalizations of UR, LUR and R respectively, which are of great significance in Banach space theory. While in Orlicz–Lorentz function space \(\Lambda_{\varphi,\omega}^{\circ}[0,\gamma)\) equipped with the Orlicz norm, the research methods of K-UR, K-LUR and K-R are much more complicated than those of UR, LUR and R. In this paper we obtain some criteria of K-UR, K-LUR and K-R of \(\Lambda_{\varphi,\omega}^{\circ}[0,\gamma)\) by means of the norm of dual space and H_μ property of \(\Lambda_{\varphi,\omega}^{\circ}[0,\gamma)\) .

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奥尔利奇-洛伦兹空间的一些轮回性

摘要 K-UR、K-LUR 和 K-R 分别是 UR、LUR 和 R 的广义，在巴拿赫空间理论中具有重要意义。虽然在奥立兹-洛伦兹函数空间（(\Lambda_{\varphi,\omega}^{\circ}[0,\gamma)\）中配有奥立兹规范，但 K-UR、K-LUR 和 K-R 的研究方法要比 UR、LUR 和 R 复杂得多。在本文中，我们通过对偶空间的规范和 \(\Lambda_{\varphi,\omega}^{\circ}[0,\gamma)\) 的 Hμ 属性，得到了 \(\Lambda_{\varphi,\omega}^{\circ}[0,\gamma)\) 的 K-UR、K-LUR 和 K-R 的一些判据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.