75 citations · 118 across the 9 of their papers we have counts for
13 papers
Improved weighted bounds for the strong maximal function
Sheldy Ombrosi, Guillermo Rey
We improve the exponents of the constant in the strong and weak-type weighted bounds for the strong maximal function, for every and every dimension …
An antichain approach to a conjecture of Zygmund
Guillermo Rey
An antichain is a family of rectangles in which no member contains another. Given a family of rectangles, let be the sum of the indicator functions…
Pairwise meets of antichains in
Guillermo Rey
The meet of two points in is their coordinatewise minimum. We show that every finite antichain in has at least distinct pairwi…
Merryfield's inequality for multiparameter martingales
Guillermo Rey
We extend an inequality of Merryfield, valid in the continuous setting, to discrete multiparameter martingales. As a consequence, we obtain the comparison of the maximal func…
Weak-type maximal function estimates on the infinite-dimensional torus
Dariusz Kosz, Guillermo Rey, Luz Roncal
We prove necessary and sufficient conditions for the weak- boundedness, for , of a maximal operator on the infinite-dimensional torus. In the endpoint case $…
Weighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces
Zoe Nieraeth, Guillermo Rey
In this paper we prove sharp weighted BMO estimates for singular integrals, and we show how such estimates can be extrapolated to Banach function spaces.
Greedy approximation algorithms for sparse collections
Guillermo Rey
We describe a greedy algorithm that approximates the Carleson constant of a collection of general sets. The approximation has a logarithmic loss in a general setting, but is optima…
Another counterexample to Zygmund's conjecture
Guillermo Rey
We present a simple dyadic construction that yields a new counterexample to Zygmund's conjecture. Our result recovers Soria's classical result in dimension three, through a differe…
Sparse domination and the strong maximal function
Alex Barron, Jose M. Conde-Alonso, Yumeng Ou +1
We study the problem of dominating the dyadic strong maximal function by -type sparse forms based on rectangles with sides parallel to the axes, and show that such dominati…
Borderline Weak Type Estimates for Singular Integrals and Square Functions
Carlos Domingo-Salazar, Michael T. Lacey, Guillermo Rey
For any Calderón-Zygmund operator , any weight , and , the operator is bounded as a map from into weak-$…
A pointwise estimate for positive dyadic shifts and some applications
Jose M. Conde-Alonso, Guillermo Rey
We prove a pointwise estimate for positive dyadic shifts of complexity which is linear in the complexity. This can be used to give a pointwise estimate for Calderón-Zygmund ope…
On the embedding of into
Guillermo Rey
We give a quantitative embedding of the Muckenhoupt class into . In particular, we show how depends on in the inequality which characterizes $A_\inf…
Extremizers and sharp weak-type estimates for positive dyadic shifts
Guillermo Rey, Alexander Reznikov
We find the exact Bellman function for the weak norm of local positive dyadic shifts. We also describe a sequence of functions, self-similar in nature, which in the limit ext…