The ℓ_p-norm of C-I, where C is the Cesàro operator

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2021-02-19 DOI:10.7153/MIA-2021-24-38

G. Jameson

引用次数: 4

Abstract

For the Cesaro operator C, it is known that ||C-I||_2 = 1. Here we prove that ||C-I||_4 < 3^(1/4) and ||C^T-I||_4 = 3. Bounds for intermediate values of p are derived from the Riesz-Thorin interpolation theorem. An estimate for lower bounds is obtained.

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C- i的p范数，其中C是Cesàro算子

对于Cesaro算子C，已知||C- i ||_2 = 1。我们证明| |我| | _4 < 3 ^(1/4)和| | C ^我| | _4 = 3。由Riesz-Thorin插值定理导出了p的中间值的边界。得到了下界的估计。

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

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.