Sharp weighted norm inequalities for Littlewood–Paley operators and singular integrals

Abstract

We prove sharp Lp(w) norm inequalities for the intrinsic square function (introduced recently by M. Wilson) in terms of the Ap characteristic of w for all 1<p<∞. This implies the same sharp inequalities for the classical Lusin area integral S(f), the Littlewood–Paley g-function, and their continuous analogs Sψ and gψ. Also, as a corollary, we obtain sharp weighted inequalities for any convolution Calderón–Zygmund operator for all 1<p⩽3/2 and 3⩽p<∞, and for its maximal truncations for 3⩽p<∞.