Alejandro Claros

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math.CA2026

From generalized PoincarÃ© to PoincarÃ©-Sobolev inequalities via self-improving methods

Alejandro Claros, Carlos PÃ©rez, Linfei Zheng

We establish several improvements to the main results of [PR19] and [CP21], refining the seminal self-improving method for generalized PoincarÃ© inequalities from [FPW98, MP98]. Th…

math.CA2026

Asymptotically sharp embedding of $A_{\infty}$ into $A_{p}$ 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 $A_{\infty}$ into $A_{p}$ with the correct asymptotic behavior when the Fujii--Wilson constant $[w]_{A_\in…

math.CA2026

Commutators of Fractional Integrals with $BMO^{2}$ Functions

You-Wei Benson Chen, Alejandro Claros

We study commutators of the Riesz potential $I_{I^} \pm$ with functions $b$ in the capacitary space $BMO^{2} (R^{n})$ , defined through the Hausdorff content $\mathcal{H}^Î²…

math.CA2025

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 $BMO$ function. More precisely, for e…

From generalized PoincarÃ© to PoincarÃ©-Sobolev inequalities via self-improving methods

Asymptotically sharp embedding of A∞​ into Ap​ for flat weights and applications to Poincaré-Sobolev inequalities

Commutators of Fractional Integrals with BMO2 Functions

Quantitative BMO-BLO Estimates for the Hardy-Littlewood Maximal Function

Asymptotically sharp embedding of $A_{\infty}$ into $A_{p}$ for flat weights and applications to Poincaré-Sobolev inequalities

Commutators of Fractional Integrals with $BMO^{2}$ Functions