On weighted norm inequalities for the Carleson operator

Abstract

We obtain $L^p(w)$ bounds for the Carleson operator $\mathcal{C}$ in terms of the $A_q$ constants $[w{]}_{A_q}$ for $1\le q\le p$. In particular, we show that, exactly as for the Hilbert transform, $\Vert \mathcal{C}{\Vert }_{L^p(w)}$ is bounded linearly by $[w{]}_{A_q}$ for $1\le q<p$. Our approach works in the general context of maximally modulated Calderón-Zygmung operators.

References in corpus (1)

• Sharp weighted estimates for classical operators