Another approach to weighted inequalities for a superposition of Copson and Hardy operators

2022/03/16 by Mustafayev, Rza, Yılmaz, Merve
#26D10 #26D15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2203.08661

Abstract

In this paper, we present a solution to the inequality ( ∫₀^∞ ( ∫_x^∞ ( ∫₀^t h )^q w(t) dt )^{r / q} u(x) ds )^1/r≤ C ( ∫₀^∞ h^p v )^{1 / p}, h ∈ \mathfrak M⁺(0,∞), using a combination of reduction techniques and discretization. Here 1 ≤ p < ∞, 0 < q , r < ∞ and u, v, w are weight functions on (0,∞).

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