Sharp two-weight, weak-type norm inequalities for singular integral operators

Abstract

We give a sufficient condition for singular integral operators and, more generally, Calderón-Zygmund operators to satisfy the weak (p, p) inequality u({x ⊂ ℝn : |T f(x)| > t}) ≤ C/tp ∫ℝn |f|Pv dx, 1 < p < ∞, δ > 0. This conditions is stronger than the Ap condition and is sharp since it fails when δ = 0.