On Carleman and Knopp's inequalities

JOURNAL OF APPROXIMATION THEORY

卷:117

Article

Kaijser, S ; Persson, LE ; Öberg, A

关键词: inequalities;    Carleman's inequality;    Knopp's inequality;    geometric means;    historical remarks;   

DOI  :  10.1006/jath.2002.3684

来源: Elsevier

【 摘 要 】

A sharpened version of Carleman's inequality is proved. This result unifies and generalizes some recent results of this type. Also the ordinary sum that serves as the upper bound is replaced by the corresponding Cesaro sum, Moreover, a Carleman-type inequality with a more general measure is proved and this result may also be seen as a generalization of a continuous variant of Carleman's inequality, which is usually referred to as Knopp's inequality. A new elementary Proof of (Carleman-)Knopp's inequality and a new inequality of Hardy-Knopp type is pointed out. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free