Weak $L^{\infty}$ and BMO in metric spaces

Details Weak $L^{\infty}$ and BMO in metric spaces Weak $L^{\infty}$ and BMO in metric spaces

2009-10-07

arxiv.org/abs/0910.1207v3

Mathematics

Metric Geometry

15 pages

Scientific paper

Bennett, DeVore and Sharpley introduced the space weak $L^{\infty}$ in 1981 and studied its relationship with functions of bounded mean oscillation. Here we characterize weak $L^{\infty}$ in measure spaces without using the decreasing rearrangement of a function. Instead, we obtain exponential estimates for the distribution function. In addition, we consider a localized version of the characterization that leads to a new characterization of BMO.

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