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

We prove sharp L^p(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<∞.