29 citations · 181 across the 37 of their papers we have counts for
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On discrete Hardy-Littlewood maximal functions over the balls in : dimension-free estimates
Jean Bourgain, Mariusz Mirek, Elias M. Stein Błażej Wróbel
We show that the discrete Hardy-Littlewood maximal functions associated with the Euclidean balls in with dyadic radii have bounds independent of the dimension on $\el…
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…
Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in
Jean Bourgain, Mariusz Mirek, Elias M. Stein +1
Dimension-free bounds will be provided in maximal and -variational inequalities on corresponding to the discrete Hardy-Littlewood averaging operators defin…