Averaging operators on decreasing or positive functions: Equivalence and optimal bounds

JOURNAL OF APPROXIMATION THEORY

卷:237

Article

Boza, Santiago¹  Soria, Javier² 

[1] Univ Politecn Cataluna, EETAC, Dept Math, E-08860 Castelldefels, Spain

[2] Univ Barcelona, Dept Math & Comp Sci, Gran Via 585, E-08007 Barcelona, Spain

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

DOI  :  10.1016/j.jat.2018.09.001

来源: Elsevier

【 摘 要 】

We study the optimal bounds for the Hardy operator S minus the identity, as well as S and its dual operator S*, on the full range 1 <= p <= infinity, for the cases of decreasing, positive or general functions (in fact, these two kinds of inequalities are equivalent for the appropriate cone of functions). For 1 < p <= 2, we prove that all these estimates are the same, but for 2 < p < infinity, they exhibit a completely different behavior. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free