Sharp weighted estimates for multi-frequency Calderón-Zygmund operators

Abstract: In this paper we study weighted estimates for the multi-frequency $\omega-$Calder\'{o}n-Zygmund operators $T$ associated with the frequency set $\Theta={\xi_1,\xi_2,\dots,\xi_N}$ and modulus of continuity $\omega$ satisfying the usual Dini condition. We use the modern method of domination by sparse operators and obtain bounds $|T|{L^p(w)\rightarrow L^p(w)}\lesssim N^{|\frac{1}{r}-\frac{1}{2}|}[w]{\mathbb{A}{p/r}}^{max(1,\frac{1}{p-r})},~1\leq r<p<\infty,$ for the exponents of $N$ and $\mathbb{A}{p/r}$ characteristic $[w]{\mathbb{A}{p/r}}$.