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Maximal inequality for high-dimensional cubes

Wednesday 19th January 2011 - 14:00 to 15:00
INI Seminar Room 1
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons