On the optimal relationships between LP-norms for the Hardy operator and its dual for decreasing functions

JOURNAL OF APPROXIMATION THEORY

卷:252

Article

Kolyada, V., I¹ 

[1] Karlstad Univ, Dept Math, Univ Gatan 1, S-65188 Karlstad, Sweden

关键词: Hardy operator;    Dual operator;    Best constants;   

DOI  :  10.1016/j.jat.2019.105362

来源: Elsevier

【 摘 要 】

We prove sharp inequalities between L-P-norms (1 < p < infinity) of functions Hf and H*f, where H is the Hardy operator, H* is its dual, and f is a nonnegative nonincreasing function on (0, infinity). In particular, we extend one result obtained for integer p >= 2 by Boza and Soria (2019), to the whole range of values p >= 2. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free