On a Refinement of Hardy’s Inequalities via Superquadratic And Subquadratic Functions - Farid, Ghulam; Krulić, Kristina; Pečarić, Josip (Sarajevo Journal of Mathematics, 2024)
Let A_k be an integral operator defined by A_kf(x):=1K(x) 2 k(x,y)f(y)d, where k:Ω_1× Ω_2 → is a general nonnegative kernel,and (Ω_1,Σ_1,μ_1), (Ω_2,Σ_2,μ_2) are measure spaces with σ-finite measures and K(x):=2 k(x,y)d, x Ω_1. In this paper we define a functional as a difference between the right-hand side and the left-hand side of the refined Hardy type inequality with general measures and kernels using the notation of superquadratic and subquadratic functions inequality and study its properties, such as exponential and logarithmic convexity. 2000 Mathematics Subject Classification. Primary 26D10, Secondary 26D15