On weighted Hardy and Poincare-type inequalities for differences

被引：13

作者：

Burenkov, VI

Evans, WD

Goldman, ML

机构：

[1] Univ Wales Coll Cardiff, Sch Math, Cardiff CF2 4AG, S Glam, Wales

[2] Tech Univ, Moscow State Inst Radio Engn Elect & Automat, Moscow, Russia

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 1997年 / 1卷 / 01期

关键词：

Hardy; Poincare; inequalities; differences;

D O I：

10.1155/S1025583497000015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A criterion is obtained for the Hardy-type inequality (integral(0)(a)\f(x)\(P)v(x)dx)(1/p) less than or equal to c(1){(v(a)integral(0)(a)\f(x)\(P)dx)(1/p) +(integral(0)(a) integral(0)(a)\f(x)-f(y)\(P)w(\x-y\)dxdy)(1/p)} to be valid for 0 < a less than or equal to A less than or equal to infinity and 0 < p < infinity. This weakens a criterion previously found by the first two authors and comes close to being necessary as well as sufficient. when an inequality in the criterion is reversed, a Poincare-type inequality is derived in some cases.

引用

页码：1 / 10

页数：10