31 citations · 156 across the 17 of their papers we have counts for
25 papers
On a multi-parameter variant of the Bellow-Furstenberg problem
Jean Bourgain, Mariusz Mirek, Elias M. Stein +1
We prove convergence in norm and pointwise almost everywhere on , , for certain multi-parameter polynomial ergodic averages by establishing the corresponding…
On regularity and irregularity of certain holomorphic singular integral operators
Loredana Lanzani, Elias M. Stein
We survey recent work and announce new results concerning two singular integral operators whose kernels are holomorphic functions of the output variable, specifically the Cauchy-Le…
On the Hardy--Littlewood maximal functions in high dimensions: Continuous and discrete perspective
Jean Bourgain, Mariusz Mirek, Elias M. Stein +1
This is a survey article about recent developments in dimension-free estimates for maximal functions corresponding to the Hardy--Littlewood averaging operators associated with conv…
Jump inequalities for translation-invariant operators of Radon type on
Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
We prove strong jump inequalities for a large class of operators of Radon type in the discrete and ergodic theoretical settings. These inequalities are the endpoints of the $…
A bootstrapping approach to jump inequalities and their applications
Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
The aim of this paper is to present an abstract and general approach to jump inequalities in harmonic analysis. Our principal conclusion is the refinement of -variational estima…
Jump inequalities via real interpolation
Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
Jump inequalities are the endpoint of Lépingle's inequality for -variation of martingales. Extending earlier work by Pisier and Xu we interpret these inequalities in terms…