The A_2 theorem with the Dini condition

Abstract

Let $T$ be an $L^2$-bounded operator having an $\omega$-Calderón--Zygmund kernel $K$ with a modulus of continuity $\omega$. If $\omega$ 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.

This paper has been withdrawn by the author due to a crucial error in the argument. The validity of the claimed main theorem remains open

References in corpus (1)

• Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals