Maximal functions, especially of the Hardy-Littlewood type, are one of the most important objects of study in harmonic analysis. Their Lp boundedness has been known for many decades. However, the exact values of their Lp norms are mostly unknown and already obtaining an estimate for these norms is a challenging question. In the talk I will discuss discrete counterparts of these maximal functions defined over the d-dimensional integer lattice. Systematic study of dimension-free estimates for such operators has been initiated several years ago in collaboration with Bourgain, Mirek, and Stein. I will overview existing results and present recent progress in the field. I will also mention connections to ergodic theory established via the Calderón transference principle.
Meeting ID: 852 4277 3200 Passcode: 103121