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

preprint2006arXivOpen access

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

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

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