Abstract
In this paper, we establish some new characterizations of weighted functions of dynamic inequalities containing a Hardy operator on time scales. These inequalities contain the characterization of Ariňo and Muckenhoupt when mathbb{T}=mathbb{R}, whereas they contain the characterizations of Bennett–Erdmann and Gao when mathbb{T}=mathbb{N}.
Highlights
In [10], Muckenhoupt characterized the weights such that the inequality ∞ x k 1/k 1/k k (x)(ς) dς dx ≤ C ωk(x) k(x) dx holds for all measurable ≥ 0 and the constant C is independent of
(ς ) ς x ≤ C υ(x) k(x) x ς0 on a time scale T holds for all nonnegative rd-continuous function on [ς0, b]T with ς0, b ∈ T, 1 < k ≤ q < ∞
Using the additive property of integrals [5, Theorem 1.77(iv)] on time scales, we see for any ς ∈ (ς0, ∞)T that σ (ς)
Summary
In [10], Muckenhoupt characterized the weights such that the inequality ∞ x k 1/k 1/k k (x)(ς) dς dx ≤ C ωk(x) k(x) dx holds for all measurable ≥ 0 and the constant C is independent of (here 1 < k < ∞). The characterization reduces to the condition that the nonnegative functions and In [3], Ariňo and Muckenhoupt characterized the weight function such that the inequality
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
