Weighted Norm Inequalities for the Local Sharp Maximal Function

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Commutators of singular integrals on generalized $L^p$ spaces with variable exponent (2004, methodology): “This inequality was proved in [ 16, Theorem 3 ]. It follows easily by putting Tf in place of ’ in Theorem 2.6 and by using Proposition 2.3 along with Theorem 2.4.”
Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture (2007, background): “The first estimate is due to Lerner [26].”
Sharp A1 Bounds for Calderón-Zygmund Operators and the Relationship with a Problem of Muckenhoupt and Wheeden (2008, background): “Note that actually this inequality was proved in [10] for δ = 1 but exactly the same proof gives the case 0 < δ < 1 as well.”
Sharp weighted estimates for classical operators (2010, background): “The exponent in Theorem 1.8 was first conjectured by Lerner [31] for the continuous square function; he also showed it was the best possible.”
Weighted weak-type inequalities and a conjecture of Sawyer (2005, result): “In [5] (using a result from [13]) we give a different proof of (1.”
A pointwise estimate for the local sharp maximal function with applications to singular integrals (2010, background): “In [15], it was shown that, for any measurable function f with f∗(+∞) and for any weight w, ∫ Rn |f(x)|w dx cn ∫ Rn M λnf(x)Mwdx, (1.”