|
This article is cited in 2 scientific papers (total in 2 papers)
Sharp conformally invariant Hardy-type inequalities with remainders
R. G. Nasibullin N.I. Lobachevsky Institute of Mathematics and Mechanics,
Kazan Federal University,
18 Kremlevskaya St
420008, Kazan, Tatarstan, Russia
Abstract:
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 $\mathbb{R}_+^n$. 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.
Keywords and phrases:
Hardy inequality, half space, remainder terms, hyperbolic domain, the Poincaré metric, hyperbolic radius, distance function.
Received: 19.03.2020
Citation:
R. G. Nasibullin, “Sharp conformally invariant Hardy-type inequalities with remainders”, Eurasian Math. J., 12:3 (2021), 46–56
Linking options:
https://www.mathnet.ru/eng/emj414 https://www.mathnet.ru/eng/emj/v12/i3/p46
|
Statistics & downloads: |
Abstract page: | 131 | Full-text PDF : | 49 | References: | 17 |
|