$\ell^p(\mathbf Z^d)$ boundedness for discrete operators of Radon types: maximal and variational estimates

Monday, October 12, 2015 -
3:00pm to 4:00pm
PLEASE NOTE ROOM CHANGE FROM LAST TERM:  SEMINAR WILL NOW BE HELD IN FINE 110.    In recent times - particularly the last two decades - discrete analogues in harmonic analysis have gone through a period of considerable changes and developments. This is due in part to Bourgain's pointwise ergodic theorem for the squares on $L^p(X, \mu)$ for any $p>1$. The main aim of this talk is to discuss recent developments in discrete harmonic analysis. We will be mainly concerned with $\ell^p(\mathbf Z^d)$ estimates $(p>1)$ of $r$-variations $(r>2)$ for discrete averaging operators and singular integral operators along polynomial mappings. All the results are subjects of the ongoing projects with Elias M. Stein and Bartosz Trojan.
Mariusz Mirek
Bonn University
Event Location: 
Fine Hall 110