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We prove an extrapolation theorem saying that the weighted weak type (1,1) inequality for A1 weights implies the strong Lp(w) bound in terms of the Lp(w) operator norm of the maximal operator M. The weak Muckenhoupt–Wheeden conjecture along with this result allows us to conjecture that the following estimate holds for a Calderón–Zygmund operator T for any p>1:‖T‖Lp(w)⩽c‖M‖Lp(w)p. The latter conjecture...
We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.
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