Weighted inequalities involving two Hardy operators

2025/06/29 by Амиран Гогатишвили, Gogatishvili, Amiran, Tuğçe Ünver +1 · 1 citation
Mathematics · #26D10 (Primary) #46E20 (Secondary) #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2506.23324

openalex publication_date 2025/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find necessary and sufficient conditions on weights u₁, u₂, v₁, v₂, i.e. measurable, positive, and finite, a.e. on (a,b), for which there exists a positive constant C such that for given 0 < p₁,q₁,p₂,q₂ <∞ the inequality \beginsplit (∫_a^b (∫_a^t f(s)^p₂ v₂(s)^p₂ ds)^{(q₂)/(p₂)} u₂(t)^q₂ dt )^(1)/(q₂)amp;
amp; \hspace-3cm≤ C (∫_a^b (∫_a^t f(s)^p₁ v₁(s)^p₁ ds)^{(q₁)/(p₁)} u₁(t)^q₁ dt )^(1)/(q₁) \endsplit holds for every non-negative, measurable function f on (a,b), where 0 ≤ a <b></b>

Citations

• New characterization of weighted inequalities involving superposition of Hardy integral operators
• Weighted inequalities involving Hardy and Copson operators
• Embeddings Between weighted local Morrey-type spaces
• Embeddings Between Weighted Cesàro Function Spaces

Cited by

• On Weighted Local Morrey-type and Complementary Local Morrey-Type Spaces

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