Cruz Uribe, DavidPérez Moreno, Carlos2016-11-142016-11-141999Cruz Uribe, D. y Pérez Moreno, C. (1999). Generalized Poincare Inequalities: sharp self-improving properties. Mathematical Research Letters, 6 (4), 417-427.1073-2780http://hdl.handle.net/11441/48500We give a sufficient condition for singular integral operators and, more generally, Calder´on-Zygmund operators to satisfy the weak (p, p) inequality u({x ∈ R n : |T f(x)| > t}) ≤ C / tp Z Rn |f|p v dx, 1 < p < ∞. Our condition is an Ap-type condition in the scale of Orlicz spaces: kukL(log L) p−1+δ,Q 1 |Q| Z Q v −p 0/p dx p/p0 ≤ K < ∞, δ > 0. This conditions is stronger than the Ap condition and is sharp since it fails when δ = 0.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/WeightsSingular integral operatorsCalderón-Zygmund operatorsMaximal operatorsOrlicz spacesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.4310/MRL.1999.v6.n4.a4