Some new characterizations of weights in dynamic inequalities involving monotonic functions
type: Item
instance of: scholarly article
title: Some new characterizations of weights in dynamic inequalities involving monotonic functions
zbMATH Open document ID: 1473.26031
author: S. H. Saker
author: Ahmed I. Saied
author: Douglas R. Anderson
published in: Qualitative Theory of Dynamical Systems
publication date: 2021-06-30T00:00:00Z
review text: In this paper, the authors derive and prove some new characterizations of weighted functions for dynamic inequalities of Hardy type involving monotonic functions on a time scale \(\mathbb{T}\) in spaces \(L^{P}(\mathbb{T})\) and \(L^{q}(\mathbb{T})\) where \(0 < p < q <\infty\) and \(p\leq 1\). The main results of this paper are given in Theorems 3.1 and 3.2 and the authors employ the reverse Hölder inequality, integration by parts, and the Fubini theorem on time scales to prove them. Several consequences of the results obtained in the cases of time scales \(\mathbb{T}= \mathbb{R}\) and \(\mathbb{T}= \mathbb{N}\) are derived and discussed. In particular, the case \(p < 1\) appears to be new. The results in this paper unify and extend continuous and discrete Hardy-type inequalities in the literature.
reviewed by: James A. Oguntuase
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26E70
zbMATH DE Number: 7365499
zbMATH Keywords: Hardy-type inequality
zbMATH Keywords: monotonic functions
zbMATH Keywords: time scales
zbMATH Keywords: weighted functions
zbMATH Keywords: inequalities
MaRDI profile type: Publication
full work available at URL: s12346-021-00489-3
OpenAlex ID: W3162211538
cites work: Weighted Norm Inequalities for Certain Integral Operators. II
cites work: Q4857830
cites work: Q5601561
cites work: Weighted Hardy and Opial-type inequalities
cites work: Boundedness of linear integral operators on a class of monotone functions
cites work: Q5439977
cites work: Q4784073
cites work: Q3997067
cites work: Weighted Hardy inequalities for decreasing sequences and functions
cites work: Hardy Type Inequalities on Time Scales
cites work: Weighted Hardy-type inequalities on time scales with applications
cites work: Q2723195
cites work: Q4797834
cites work: Minkowski and Beckenbach-Dresher inequalities and functionals on time scales
cites work: Q2947966
DOI: 10.1007/S12346-021-00489-3
description: scientific article; zbMATH DE number 7365499