Boundedness of Hardy-type operators with a kernel: integral weighted conditions for the case

被引：0

作者：

Krepela, Martin ^{[1
,2
]}

机构：

[1] Karlstad Univ, Fac Hlth Sci & Technol, Dept Math & Comp Sci, S-65188 Karlstad, Sweden

[2] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Sokolovska 83, Prague 18675 8, Czech Republic

来源：

REVISTA MATEMATICA COMPLUTENSE | 2017年 / 30卷 / 03期

关键词：

Hardy operators; Integral operators; Weighted inequalities; Weighted function spaces; REDUCTION THEOREMS; MONOTONE-FUNCTIONS; NORM INEQUALITIES; LORENTZ SPACES;

D O I：

10.1007/s13163-017-0230-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let 1 < p < infinity and 0 < q < p. We prove necessary and sufficient conditions under which the weighted inequality (integral(infinity)(0) (integral(t)(0) f(x)U(x, t) dx)(q) w(t) dt)(1/q) <= C (integral(infinity)(0) f(p)(t)v(t) dt)(1/p), where U is a so-called -regular kernel, holds for all nonnegative measurable functions f on (0, infinity). The conditions have an explicit integral form. Analogous results for the case and for the dual version of the inequality are also presented. The results are applied to close various gaps in the theory of weighted operator inequalities.

引用

页码：547 / 587

页数：41

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