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

Mariusz Mirek, Bonn University
Fine Hall 110
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.