12 citations · 18 across the 12 of their papers we have counts for
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Dimension-free estimates for discrete maximal functions over cubes in
Mariusz Mirek, Tomasz Z. Szarek, Błażej Wróbel
In this short note, we establish dimension-free bounds, for all , for the discrete Hardy--Littlewood maximal functions associated with cubes i…
A dimension-free estimate on for the maximal Riesz transform in terms of the Riesz transform
Maciej Kucharski, Błażej Wróbel
W prove a dimension-free estimate for the norm of the maximal truncated Riesz transform in terms of the norm of the Riesz transform. Consequ…
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 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…
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…