Hytönen, TuomasPérez Moreno, Carlos2016-10-102016-10-102013Hytönen, T. y Pérez Moreno, C. (2013). Sharp weighted bounds involving A∞. Analysis and PDE, 6 (4), 777-818.2157-50451948-206Xhttp://hdl.handle.net/11441/47242We improve on several weighted inequalities of recent interest by replacing a part of the Ap bounds by weaker A∞ estimates involving Wilson’s A∞ constant [w] 0 A∞ := sup Q 1 / w(Q) Z Q M(wχQ). In particular, we show the following improvement of the first author’s A2 theorem for Calderón-Zygmund operators T : kT kB(L2(w)) ≤ cT [w] 1/2 A2 [w] 0 A∞ + [w −1] 0 A∞ 1/2. Corresponding Ap type results are obtained from a new extrapolation theorem with appropriate mixed Ap A∞ bounds. This uses new two-weight estimates for the maximal function, which improve on Buckley’s classical bound.We also derive mixed A1-A∞ type results of Lerner, Ombrosi and Pérez (2009) of the form kT kB(L p(w)) ≤ cpp0 [w] 1/p A1 ([w] 0 A∞ ) 1/p 0 , 1 < p < ∞, kT f kL 1,∞(w) ≤ c[w]A1 log(e + [w] 0 A∞ )k f kL 1(w). An estimate dual to the last one is also found, as well as new bounds for commutators of singular integralsapplication/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Weighted norm inequalitiesAp weightsSharp estimatesMaximal functionCalderón-Zygmund operatorsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.2140/apde.2013.6.777