New characterization of weighted inequalities involving superposition of Hardy integral operators

2024/06/17 by Амиран Гогатишвили, Gogatishvili, Amiran, Tuğçe Ünver +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2406.11298

Abstract

Let 1≤ p <∞ and 0 < q,r < ∞. We characterize the validity of the inequality for the composition of the Hardy operator, (∫_a^b (∫_a^x (∫_a^t f(s)ds )^q u(t) dt )^(r)/(q) w(x) dx )^(1)/(r) ≤ C (∫_a^b f(x)^p v(x) dx )^(1)/(p) for all non-negative measurable functions f on (a,b), -∞ ≤ a < b ≤ ∞. We construct a more straightforward discretization method than those previously presented in the literature, and we provide some new scales of weight characterizations of this inequality in both discrete and continuous forms and we obtain previous characterizations as the special case of the parameter.

Cited by

• Weighted inequalities involving two Hardy operators

Related

• Weighted inequalities involving iteration of two Hardy integral operators
• Another approach to weighted inequalities for a superposition of Copson and Hardy operators
• Weighted inequalities involving two Hardy operators
• The two-weight Hardy inequality: a new elementary and universal proof
• Weighted inequalities involving Hardy and Copson operators