𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Some Sharp Reversed Hölder and Hardy Type Inequalities

✍ Scribed by Jöran Bergh; Victor Burenkov; Lars Erik Persson

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
464 KB
Volume
169
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We discuss some reversed Hölder inequalities yielding for functions on R~+~ satisfying one or two conditions of quasi‐monotonicity. All cases of equality are pointed out. By using these results and some recent results by the present authors (see [3]), we prove some new reversed inequalities of Hardy type for quasi‐monotone functions. In some cases we obtain the best constants and all cases of equality are obtained. Some applications, open questions and the relations to other similar results are pointed out.

📜 SIMILAR VOLUMES

Reverse Hölder Inequalities and Approxim
Reverse Hölder Inequalities and Approximation Spaces
✍ Joaquim Martı́n; Mario Milman 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 193 KB

We develop a simple geometry free context where one can formulate and prove general forms of Gehring's Lemma. We show how our result follows from a general inverse type reiteration theorem for approximation spaces.

On Hardy—Type Inequalities
On Hardy—Type Inequalities
✍ D. E. Edmunds; R. Hurri-Syrjänen 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 379 KB

We show that certain Hardy-type inequalities hold in plump domains and domains with a Whitney cube #-condition. 1991 Mathematics Subject Classification. 46E35, 26D 10.

Remark on Inequalities between Hölder an
Remark on Inequalities between Hölder and Lehmer Means
✍ Zheng Liu 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 87 KB

In 1 Stolarsky established an inequality between the two variable w x means of Holder and Lehmer that is much stronger than that given in 2 . ¨w x However, it should be noted that the inequalities given in 2 are in connection with more general n-variable means. So, it is natural to ask if we could

The Monotonic Property of Ls(μ)-Averagin
The Monotonic Property of Ls(μ)-Averaging Domains and Weighted Weak Reverse Hölder Inequality
✍ Bing Liu; Shusen Ding 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 87 KB

We first prove a local weighted weak reverse Holder inequality for A-harmonic ¨sŽ . tensors. Then, we study the monotonic property of newly introduced L -averaging domains, which can be viewed as an application of the local weighted reverse s Ž . Holder inequality in L -averaging domains. By applyi