0564898 - MÚ 2023 RIV DE eng J - Journal Article
Gogatishvili, Amiran - Pick, L. - Tuğçe, Ü.
Weighted inequalities for discrete iterated kernel operators.
Mathematische Nachrichten. Roč. 295, č. 11 (2022), s. 2171-2196. ISSN 0025-584X. E-ISSN 1522-2616
R&D Projects: GA ČR(CZ) GA18-00580S
Institutional support: RVO:67985840
Keywords : weighted inequality * kernel operator * supremum operator
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1002/mana.202000144

We develop a new method that enables us to solve the open problem of characterizing discrete inequalities for kernel operators involving suprema. More precisely, we establish necessary and sufficient conditions under which there exists a positive constant C such that (Formula presented.) holds for every sequence of nonnegative numbers (Formula presented.) where U is a kernel satisfying certain regularity condition, (Formula presented.) and (Formula presented.) and (Formula presented.) are fixed weight sequences. We do the same for the inequality (Formula presented.) We characterize these inequalities by conditions of both discrete and continuous nature.
Permanent Link: https://hdl.handle.net/11104/0336468