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arXiv · 1610.00444

Sharp weighted estimates for multi-frequency Calder\'on-Zygmund operators

Saurabh Shrivastava·K. S. Senthil Raani
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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 $[w]_{\mathbb{A}_{p/r}}$.

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Saurabh Shrivastava, K. S. Senthil Raani. 2016-10-03. Sharp weighted estimates for multi-frequency Calder\'on-Zygmund operators. https://arxiv.org/abs/1610.00444

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