Weighted inequalities for a superposition of the Copson operator and the Hardy operator

0555455 - MÚ 2023 RIV US eng J - Journal Article
Gogatishvili, Amiran - Mihula, Z. - Pick, L. - Turčinová, H. - Tuğçe, Ü.
Weighted inequalities for a superposition of the Copson operator and the Hardy operator.
Journal of Fourier Analysis and Applications. Roč. 28, č. 2 (2022), č. článku 24. ISSN 1069-5869. E-ISSN 1531-5851
R&D Projects: GA ČR(CZ) GA18-00580S
Institutional support: RVO:67985840
Keywords : weighted Hardy inequality * superposition of operators * Copson operator
OECD category: Pure mathematics
Impact factor: 1.2, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s00041-022-09918-6

We study a three-weight inequality for the superposition of the Hardy operator and the Copson operator in weighted Lebesgue spaces all possible positive real parameters. A simple change of variables can be used to equaivalently turn this inequality into the one in which the Hardy and Copson operators swap their positions. We focus on characterizing those triples of weight functions for which the inequality holds for all nonnegative measurable functions with a constant independent of function. We use a new type of approach based on an innovative method of discretization which enables us to avoid the duality technique.
Permanent Link: http://hdl.handle.net/11104/0329970