RT Journal Article
T1 Quantitative John–Nirenberg inequalities at different scales
A1 Martínez-Perales, Javier Cecilio
A1 Rela, Ezequiel
A1 Rivera Ríos, Israel P.
K1 Desigualdades isoperimétricas
AB Given a family Z = { · Z Q } of norms or quasi-norms with uniformly boundedtriangle inequality constants, where each Q is a cube in Rn, we provide an abstractestimate 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 abstractscheme allows us to recover the sharp estimate f − fQ,μL pQ, dμ(x)μ(Q) ≤ c(μ)p f BMO(dμ), p ≥ 1for every cube Q and every f ∈ BMO(dμ), which is known to be equivalent tothe 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
PB Springer
YR 2022
FD 2022-06-07
LK https://hdl.handle.net/10630/24649
UL https://hdl.handle.net/10630/24649
LA eng
NO 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
NO J. C. M.-P. is supported by the Basque Government through the BERC 2018-2021program and by Spanish Ministry of Science, Innovation and Universities through BCAM Severo Ochoaaccreditation SEV-2017-0718. He is also supported by MINECO through the MTM2017-82160-C2-1-Pproject funded by (AEI/FEDER, UE), acronym “HAQMEC”, through ”la Caixa” Grant, and through theMATHROCKS project, funded by European Commission with Grant Agreement Number 777778 (H2020-MSCA-RISE-2017). He is also grateful to the people of the Universidad de Buenos Aires and the UniversidadNacional del Sur for their hospitality during his visit to Argentina in 2019. E.R. is partially supported byGrants UBACyT 20020170200057BA and PIP (CONICET) 11220110101018. This project has receivedfunding from the European Union’s Horizon 2020 research and innovation programme under the MarieSklodowska-Curie Grant agreement No 777822. I.P.R.-R. is partially supported by Grants PICT 2018-02501and PICT 2019-00018 (Agencia I+D+i) and by Grant UMA18-FEDERJA-002 (FEDER).Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Funding for open access charge: Universidad de Málaga / CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026