Sharp weighted estimates for multi-frequency Calderón-Zygmund operators

Abstract

In this paper we study weighted estimates for the multi-frequency $\omega -$Calderón-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 $\Vert T{\Vert }_{L^p(w)\to L^p(w)}\lesssim N^{|\frac{1}{r}-\frac{1}{2}|}[w{]}_{{\mathbb{A}}_{p/r}}^{max(1,\frac{1}{p-r})},1\le r<p<\infty ,$ for the exponents of $N$ and ${\mathbb{A}}_{p/r}$ characteristic $[w{]}_{{\mathbb{A}}_{p/r}}$.

Mistake in argument

References in corpus (1)

• On pointwise estimates involving sparse operators