Sharp weighted estimates for vector-valued singular integral operators and commutators

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Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture (2007, background): “Vector-valued singular integrals satisfy essentially the same inequality [38]: if 0 < q < 1 and 1 < r < ∞ there exists a constant such that M q ( ‖{Tfj}j‖`r ) (x) ≤ C M ( ‖{fj}j‖`r ) (x).”