Gogatishvili, AmiranMustafayev, Rza Ch.2020-06-252020-06-252017Gogatishvili, Amiran & Mustafayev, Rza. (2017). Weighted iterated Hardy-type inequalities. Mathematical Inequalities & Applications. 20. 683-728. 10.7153/mia-2017-20-45.1331-4343https://doi.org/10.7153/mia-20-45https://hdl.handle.net/20.500.12587/6940Gogatishvili, Amiran/0000-0003-3459-0355; Gogatishvili, Amiran/0000-0003-3459-0355; Mustafayev, Rza/0000-0002-2806-9646In this paper 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.eninfo:eu-repo/semantics/openAccessQuasilinear operatorsiterated Hardy inequalitiesweightsArticle20368372810.7153/mia-20-452-s2.0-85020772283Q1WOS:000412831000004Q3