Séminaire Orléans

Discrete operators of Radon type
Bartosz Trojan (Polish Academy of Science)
Thursday 26 October 2017 14:00 -  Orléans -  Salle de Séminaire

Résumé :
In mid 80s Bourgain published a series of papers proving pointwise ergodic theorems for averaging operators over thin subsets of integers. In particular, the article studding ergodic averages over {n^2 : n ∈ N} for functions in L^p(X, μ), p > 1, has started the dynamical development of discrete harmonic analysis. The aim of this talk is to discuss some recent achievements. We will be mainly concerned with l^p(Z^d) , p > 1, estimates for maximal functions and r-variations, r > 2, for discrete averaging operators and singular integral operators along polynomial mappings on Z^k or P^k. The talk will be based on a joint work with Elias M. Stein and Mariusz Mirek.

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