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arXiv · 1310.3352

On weighted norm inequalities for the Carleson operator

Andrei K. Lerner
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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, $\|{\mathcal C}\|_{L^p(w)}$ 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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Andrei K. Lerner. 2013-10-12. On weighted norm inequalities for the Carleson operator. https://arxiv.org/abs/1310.3352

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