Abstract
The purpose of this paper is twofold. In the first place, we extend some of the recent results of Jawerth and Torchinskyty concerning local maximal functions in R~n to the more general context of spaces of homogeneous type. The John-Nirenberg inequality is contained in our results. In the second place, we shall discuss the BMOlogk spaces considered by Long Ruilin and Yang Lo[2]. This we achieve by introducing an appropriate local sharp maximal function.
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