2026-05-28T23:25:00Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/246492026-02-03T11:00:02Zcom_10630_2254col_10630_37953

Quantitative John–Nirenberg inequalities at different scales Martínez-Perales, Javier Cecilio Rela, Ezequiel Rivera Ríos, Israel P. Desigualdades isoperimétricas Given a family Z = { · Z Q } of norms or quasi-norms with uniformly bounded triangle inequality constants, where each Q is a cube in Rn, we provide an abstract estimate of the form f − fQ,μZ Q ≤ c(μ)ψ(Z) f BMO(dμ) for every function f ∈ BMO(dμ), where μ is a doubling measure in Rn and c(μ) and ψ(Z) are positive constants depending on μ and Z, respectively. That abstract scheme allows us to recover the sharp estimate f − fQ,μL p Q, dμ(x) μ(Q) ≤ c(μ)p f BMO(dμ), p ≥ 1 for every cube Q and every f ∈ BMO(dμ), which is known to be equivalent to the John–Nirenberg inequality, and also enables us to obtain quantitative counterparts when L p is replaced by suitable strong and weak Orlicz spaces and L p(·) spaces. Besides the aforementioned results we also generalize [(Ombrosi in Isr J Math 238:571-591, 2020), Theorem 1.2] to the setting of doubling measures and obtain a new characterization of Muckenhoupt’s A∞ weights 2022-07-12T12:01:40Z 2022-07-12T12:01:40Z 2022-06-07 journal article Cite this article Martínez-Perales, J.C., Rela, E. & Rivera-Ríos, I.P. Quantitative John–Nirenberg inequalities at different scales. Rev Mat Complut (2022). https://doi.org/10.1007/s13163-022-00427-0 https://hdl.handle.net/10630/24649 https://doi.org/10.1007/s13163-022-00427-0 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer