180 citations · 947 across the 92 of their papers we have counts for
118 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…
Decouplings for Real Analytic Surfaces of Revolution
Jean Bourgain, Ciprian Demeter, Dominique Kemp
We extend the decoupling results of the first two authors to the case of real analytic surfaces of revolution in . New examples of interest include the torus and the…
Anderson localization for two interacting quasiperiodic particles
Jean Bourgain, Ilya Kachkovskiy
We consider a system of two discrete quasiperiodic 1D particles as an operator on and establish Anderson localization at large disorder, assuming the potentia…
On the number of th powers inside arithmetic progressions
Jean Bourgain, Ciprian Demeter
We find upper bounds that are sharp for the number of th powers inside arbitrary arithmetic progressions whose step has many divisors.
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…