On the Hardy-Littlewood maximal function for the cube
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In this article, it was shown that the Hardy-Littlewood maximal function associated to the cube in ℝ n ≥ 1 obeys dimensional free bounds in L p ≥ 1 for p > 1.Abstract:
It is shown that the Hardy-Littlewood maximal function associated to the cube in ℝ
n
obeys dimensional free bounds in L
p
for p > 1. Earlier work only covered the range p > $$\frac{3}{2}$$
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A bootstrapping approach to jump inequalities and their applications
TL;DR: In this paper, an abstract and general approach to jump inequalities in harmonic analysis is presented, which is applied to the dimension-free results recently obtained by the first two authors in collaboration with Bourgain, and also to operators of Radon type treated by Jones, Seeger, and Wright.
Journal ArticleDOI
Dimension free bounds for the Hardy–Littlewood maximal operator associated to convex sets
TL;DR: A survey of maximal functions inequalities for convex sets in high dimensional linear spaces can be found in this paper, where Bourgain, Carbery and Muller present several results along this line, and a new one due to Bourgain (2014).
Journal ArticleDOI
On dimension-free variational inequalities for averaging operators in $\mathbb R^d$
TL;DR: In this article, the dimension-free L p ≥ 2 inequalities for r-variations of the Hardy-Littlewood averaging operator defined over symmetric convex bodies were studied.
Journal ArticleDOI
Dimension-Free Estimates for Discrete Hardy-Littlewood Averaging Operators Over the Cubes in ℤd
TL;DR: In this article, dimension-free bounds for discrete Hardy-Littlewood averaging operators over the cubes in a convex body were provided in maximal and $r$-variational inequalities.
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Pointwise convergence of noncommutative fourier series
TL;DR: In this paper, the pointwise convergence of Fourier series for non-abelian compact groups, group von Neumann algebras and quantum groups is studied and a non-commutative bootstrap method is developed.
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