Sharp weighted estimates for multi-frequency Calderón-Zygmund operators

Saurabh Shrivastava, Senthil Raani K. S

Published 2016-10-03Version 1

In this paper we study weighted estimates for the multi-frequency $\omega-$Calder\'on-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 sharp bounds $\|T\|_{L^p(w)\rightarrow L^p(w)}\lesssim N^{\frac{1}{2}}[w]_{\mathbb{A}_p}^{max(1,\frac{1}{p-1})}$ for the exponents of $N$ and $\mathbb{A}_p$ characteristic $[w]_{\mathbb{A}_p}$.