Dimension dependency of the weak type $(1,1)$ bounds for maximal functions associated to finite radial measures

Mathematics – Classical Analysis and ODEs

Scientific paper

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7 pages, to appear in the Bull. London Math. Soc

Scientific paper

We show that the best constants appearing in the weak type (1,1) inequalities
satisfied by the centered Hardy-Littlewood maximal function associated to some
finite radial measures, such as the standard gaussian measure, grow
exponentially fast with the dimension.

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