Weighted iterated Hardy-type inequalities

0474670 - MÚ 2018 RIV HR eng J - Journal Article
Gogatishvili, Amiran - Mustafayev, R.Ch.
Weighted iterated Hardy-type inequalities.
Mathematical Inequalities & Applications. Roč. 20, č. 3 (2017), s. 683-728. ISSN 1331-4343. E-ISSN 1331-4343
R&D Projects: GA ČR GA13-14743S
Institutional support: RVO:67985840
Keywords : quasilinear operators * iterated Hardy inequalities * weights
OECD category: Pure mathematics
Impact factor: 0.649, year: 2017
http://files.ele-math.com/preprints/mia-20-45.pdf

In 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.
Permanent Link: http://hdl.handle.net/11104/0271669