On weighted norm inequalities for the Carleson operator

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, $\|{\mathcal C}\|_{L^p(w)}$ 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.

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