Some New Characterizations of Weights in Dynamic Inequalities Involving Monotonic Functions

• Saker, Samir H. ^[1] ; Saied, Ahmed I. ^[2] ; Anderson, Douglas R. ^[3]
  1. [1] Galala University & Mansoura University
  2. [2] Benha University
  3. [3] Concordia College (Moorhead)

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 2, 2021
• Idioma: inglés
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  • 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 L p(T) and Lq (T) when 0 < p < q < ∞ and p ≤ 1. The main results will be proved by employing the reverse Hölder 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