Geodesic
Weak $L^\infty$ and BMO in Metric Spaces
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 2, pp. 369-385 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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 the weak $L^{\infty}$ in measure spaces without using the decreasing rearrangement of a function. Instead, we use exponential estimates for the distribution function. In addition, we consider a localized version of the characterization that leads to a new characterization of BMO. 
@article{BUMI_2012_9_5_2_a10,
     author = {Aalto, Daniel},
     title = {Weak $L^\infty$ and {BMO} in {Metric} {Spaces}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {369--385},
     year = {2012},
     volume = {Ser. 9, 5},
     number = {2},
     zbl = {1256.46013},
     mrnumber = {2977254},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_2_a10/}
}
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Aalto, Daniel. Weak $L^\infty$ and BMO in Metric Spaces. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 2, pp. 369-385. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_2_a10/