SHARP CONFORMALLY INVARIANT HARDY-TYPE INEQUALITIES WITH REMAINDERS

被引：2
|
作者：
Nasibullin, R. G. [1 ]
机构：
[1] Kazan Fed Univ, NI Lobachevsky Inst Math & Mech, 18 Kremlevskaya St, Kazan 420008, Tatarstan, Russia
来源：
EURASIAN MATHEMATICAL JOURNAL | 2021年 / 12卷 / 03期
基金：
俄罗斯科学基金会;
关键词：
Hardy inequality; half space; remainder terms; hyperbolic domain; the Poincare metric; hyperbolic radius; distance function; GEOMETRICAL VERSION; INTEGRAL-INEQUALITIES; DOMAINS; CONSTANTS; EXPONENT; SPACE;
D O I：
10.32523/2077-9879-2021-12-3-46-56
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the present paper we establish new Hardy-Maz'ya-type inequalities with remainders for all continuously differentiable functions with compact support in the half space R. The weight functions depend on the distance to the boundary or on the distance to the origin. Also new sharp Avkhadiev-Hardy-type inequalities involving the distance to the boundary or the hyperbolic radius are proved. We consider Avkhadiev-Hardy-type inequalities in simply and doubly connected plain domains and in tube-domains.
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页码：46 / 56
页数：11
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