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Maximal operators and decoupling for $\Lambda(p)$ Cantor measures
TL;DR: In this paper, a decoupling inequality similar to that of Laba and Wang was used to construct a Cantor-type measure on R supported on sets of Hausdorff dimensions.
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Abstract: For $2\leq p 2/p$, and $\delta>0$, we construct Cantor-type measures on $\mathbb{R}$ supported on sets of Hausdorff dimension $\alpha 0$, and have no Fourier decay. The proof is based on a decoupling inequality similar to that of Laba and Wang.
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Citations
New bounds on Cantor maximal operators
TL;DR: In this article , it was shown that the maximal operators associated with an Ahlfors-regular variant of fractal percolation are bounded on a constant factor of the dimension of the Salem Cantor set.
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New bounds on Cantor maximal operators
Pablo Shmerkin,Ville Suomala +1 more
TL;DR: In this article, it was shown that the maximal operators associated with an Ahlfors-regular variant of fractal percolation are bounded on a constant factor of the dimension of the Salem Cantor set.
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The proof of the l 2 Decoupling Conjecture
Jean Bourgain,Ciprian Demeter +1 more
TL;DR: In this article, the l 2 decoupling conjecture for compact hypersurfaces with positive denite second fundamental form and also for the cone was shown to hold for both rational and irrational torus.
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Solving a linear equation in a set of integers I
TL;DR: In this paper, the vanishing of the constant term b and the sum of coefficients s = a1 +... + ak had a strong effect on the behaviour of equation (1.1).