We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderón-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-1-2, author = {Daniel Aalto and Lauri Berkovits and Outi Elina Kansanen and Hong Yue}, title = {John-Nirenberg lemmas for a doubling measure}, journal = {Studia Mathematica}, volume = {204}, year = {2011}, pages = {21-37}, zbl = {1230.43006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-1-2} }
Daniel Aalto; Lauri Berkovits; Outi Elina Kansanen; Hong Yue. John-Nirenberg lemmas for a doubling measure. Studia Mathematica, Tome 204 (2011) pp. 21-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-1-2/