Weighted integral inequalities with the geometric mean operator

被引：56

作者：

Persson, LE ^{[1
]}

Stepanov, VD

机构：

[1] Univ Lulea, Dept Math, S-97187 Lulea, Sweden

[2] Russian Acad Sci, Ctr Comp, Far Eastern Branch, Khabarovsk 680042, Russia

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2002年 / 7卷 / 05期

关键词：

geometric mean operator; Hardy inequalities;

D O I：

10.1080/1025583021000022531

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The geometric mean operator is defined by Gf(x) = exp(1/xintegral(0)(x) log f(t)dt). A precise two-sided estimate of the norm parallel toGparallel to = sup(fnot equal0) parallel toGfparallel toL(p)(q)/parallel tofparallel toL(v)(p) for 0 < p, g less than or equal to infinity is given and some applications and extensions are pointed out.

引用

页码：727 / 746

页数：20

共 14 条

[1]

BLISS GA, 1930, J LOND MATH SOC, V5, P40

[2]

Carleman T., 1923, C FAITES CINQUIEMECO, P181

[3] INEQUALITIES RELATED TO HARDY AND HEINIG [J].