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Dimension-free estimates for discrete maximal functions related to normalized gaussians
Mariusz Mirek, Tomasz Z. Szarek, Błażej Wróbel
In this paper, we investigate dimension-free estimates for maximal operators of convolutions with discrete normalized Gaussians (related to the Theta function) in the context of ma…
Dimension-free estimates for the discrete spherical maximal functions
Mariusz Mirek, Tomasz Z. Szarek, Błażej Wróbel
We prove that the discrete spherical maximal functions (in the spirit of Magyar, Stein and Wainger) corresponding to the Euclidean spheres in with dyadic radii have $…
Some remarks on dimension-free estimates for the discrete Hardy-Littlewood maximal functions
Dariusz Kosz, Mariusz Mirek, Paweł Plewa +1
Dependencies of the optimal constants in strong and weak type bounds will be studied between maximal functions corresponding to the Hardy--Littlewood averaging operators over conve…
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…
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…