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Almost everywhere convergence of averages
Laurent Moonens(Université Paris-Sud)
2019年1月2日至10日 10:00-11:00  闵行数学楼102报告厅

(1) Colloquium : ? In this first talk we shall describe some general principles in the theory of Lebesgue differentiation, see how the validity in general frameworks of a Lebesgue-type differentiation theorem relates to property of some associated operator, before to focus our attention on the delicate issue of differentiating along rectangles ?.

(2) Lectures : ? After recalling some classical material from Harmonic Analysis and basic Geometric Measure Theory, we shall start by some general necessary and sufficient conditions on a sequence of averaging operators, in order for them to converge almost everywhere in a given function space. This will allow us to discuss interesting positive and negative results for ergodic, Lebesgue and convolution averaging processes.

Host: Prof. Thierry De Pauw