6 papers
From generalized Poincaré to Poincaré-Sobolev inequalities via self-improving methods
Alejandro Claros, Carlos Pérez, Linfei Zheng
We establish several improvements to the main results of [PR19] and [CP21], refining the seminal self-improving method for generalized Poincaré inequalities from [FPW98, MP98]. Th…
Asymptotically sharp embedding of into for flat weights and applications to Poincaré-Sobolev inequalities
Alejandro Claros, Ezequiel Rela
We provide new quantitative results on the embedding of the Muckenhoupt class into with the correct asymptotic behavior when the Fujii--Wilson constant $[w]_{A_\in…
Bourgain-Brezis-Mironescu formula for Riesz Potentials
Alejandro Claros, Carlos Pérez
We identify the Bourgain-Brezis-Mironescu pointwise limit of the nonlocal potential operator , , where denotes the Riesz potential and…
Commutators of Fractional Integrals with Functions
You-Wei Benson Chen, Alejandro Claros
We study commutators of the Riesz potential with functions in the capacitary space , defined through the Hausdorff content $\mathcal{H}^β…
Quantitative BMO-BLO Estimates for the Hardy-Littlewood Maximal Function
Alejandro Claros
In this note, we study a quantitative extension of the John-Nirenberg inequality for the Hardy-Littlewood maximal function of a function. More precisely, for e…
-dimensional sharp maximal function and applications
You-Wei Benson Chen, Alejandro Claros
In this paper, we study -dimensional sharp maximal operator defined as \begin{align*} \mathcal{M}^{\#} _βf(x) := \sup_{Q} \inf_{c \in \mathbb{R}} Ï_{Q}(x) \frac{1}{\ell(Q)^β…