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math.CA2026
Pointwise Riesz potential bounds for rough singular integrals
Kabe Moen, Carlos Pérez
We give a complete characterization of the kernels $Ω\in \Lup^1(\mathbb S^{d-1})$ for which the rough singular integral $\T_Ω$ and its associated maximal operator $\M_Ω$ satisfy po…
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 , , where denotes the Riesz potential and $\ma…