2015/03/13 by Амиран Гогатишвили, Amiran Gogatishvili, Gogatishvili, Amiran +2
Mathematics · #26D10 #26D15 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #math.AP #math.CA #math.FA #msc:26D10 #msc:26D15
paper · pdf · doi:10.48550/arxiv.1503.04079
arxiv created 2015/03/13 · openalex publication_date 2015/03/13 · arxiv updated 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator T with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for the operator T to be bounded in weighted Lebesgue spaces restricted to the cones of monotone functions, which allow to change the cone of non-decreasing functions to the cone of non-increasing functions and vice versa not changing the operator T. New characterizations of the weighted Hardy-type inequalities on the cones of monotone functions are given. The validity of so-called weighted iterated Hardy-type inequalities are characterized.