Alejandro Claros

activity

20242026

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4 papers · 1 filter

math.CA2026

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]. The…

math.AP2026

Bourgain-Brezis-Mironescu formula for Riesz Potentials

Alejandro Claros, Carlos Pérez

We identify the Bourgain-Brezis-Mironescu pointwise limit of the nonlocal potential operator $(1 - α) I_{α} (D^{α} f)$ , $0 < α < 1$ , where $I_{α}$ denotes the Riesz potential and $\ma…

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 $BMO^{β}$ Functions

You-Wei Benson Chen, Alejandro Claros

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

From generalized Poincaré to Poincaré-Sobolev inequalities via self-improving methods

Bourgain-Brezis-Mironescu formula for Riesz Potentials

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

Commutators of Fractional Integrals with BMOβ Functions

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

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