BMO from dyadic BMO for nonhomogeneous measures

Autores: José Manuel Conde Alonso
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 64, Nº 1, 2020, págs. 353-372
Idioma: inglés
DOI: 10.5565/publmat6412014
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Resumen
- The usual one third trick allows to reduce problems involving general cubes to a countable family. Moreover, this covering lemma uses only dyadic cubes, which allows to use nice martingale properties in harmonic analysis problems. We consider alternatives to this technique in spaces equipped with nonhomogeneous measures. This entails additional diﬃculties which force us to consider martingale ﬁltrations that are not regular. The dyadic covering that we ﬁnd can be used to clarify the relationship between martingale BMO spaces and the most natural BMO space in this setting, which is the space RBMO introduced by Tolsa.