Some New Characterizations of Weights in Dynamic Inequalities Involving Monotonic Functions

被引：9

作者：

Saker, Samir H. ^{[1
,2
]}

Saied, Ahmed, I ^{[3
]}

Anderson, Douglas R. ^{[4
]}

机构：

[1] Galala Univ, Fac Sci, Dept Math, Galala New City, Egypt

[2] Mansoura Univ, Fac Sci, Dept Math, Mansoura, Egypt

[3] Benha Univ, Dept Math Fac Sci, Banha, Egypt

[4] Concordia Coll, Dept Math, Moorhead, MN 56562 USA

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2021年 / 20卷 / 02期

关键词：

Hardy's type inequality; Monotonic functions; Time scales; Weighted functions; Inequalities; HARDY;

D O I：

10.1007/s12346-021-00489-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove some new characterizations of weighted functions for dynamic inequalities of Hardy's type involving monotonic functions on a time scale T in different spaces Lp(T) and Lq(T) when 0<p<q<infinity and p <= 1. The main results will be proved by employing the reverse Holder inequality, integration by parts, and the Fubini theorem on time scales. The main contribution in this paper is the new proof in the case when p<1, which has not been considered before on time scales. Moreover, the results unify and extend continuous and discrete systems under one theory.

引用

页数：22

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[1] Some New Characterizations of Weights in Dynamic Inequalities Involving Monotonic Functions
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[10] New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations
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