### Maximal inequality for high-dimensional cubes

Aubrun, G *(Lyon)*

Wednesday 19 January 2011, 14:00-15:00

Seminar Room 1, Newton Institute

#### Abstract

The talk will deal with the behaviour of the best constant in the Hardy-Littlewood maximal inequality in R^n when the dimension goes to infinity. More precisely, I will sketch a simple probabilistic proof of the following result (due to Aldaz): when the maximal function is defined by averaging over all centred cubes, the Hardy-Littlewood inequality does not hold with a constant independent of the dimension.

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