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We improve on several weighted inequalities of recent interest by replacing a part of the math bounds by weaker math estimates involving Wilson’s math constant¶∞′: = sup1 () ∫ (χ). ¶ In particular, we show the following improvement of the first author’s math theorem for Calderón–Zygmund operators math: ¶∥∥ℬ (2 () ) ≤21∕2 (∞′+−1∞′) 1∕2. ¶ Corresponding math type results are obtained from a new extrapolation theorem with appropriate mixed math - math bounds. This uses new two-weight estimates for the maximal function, which improve on Buckley’s classical bound. ¶ We also derive mixed math - math type results of Lerner, Ombrosi and Pérez (2009) of the form¶∥∥ℬ ( () ) ≤′11∕ (∞′) 1∕′, 1∞, ∥∥1, ∞ () ≤1 log (+[</
Hytönen et al. (Wed,) studied this question.