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arXiv · 1212.3842

The A_2 theorem with the Dini condition

Tuomas P. Hytönen
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Abstract

Let $T$ be an $L^2$-bounded operator having an $ω$-Calderón--Zygmund kernel $K$ with a modulus of continuity $ω$. If $ω$ satisfied the Dini condition $\int_0^1ω(t)\ud t/t<\infty$, then $T$ satisfies the $A_2$ theorem $$ \Norm{Tf}{L^2(w)}\lesssim [w]_{A_2}\Norm{f}{L^2(w)} $$ and many related estimates, as a consequence of a domination by dyadic operators.

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Tuomas P. Hytönen. 2013-04-29. The A_2 theorem with the Dini condition. https://arxiv.org/abs/1212.3842

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