"Small step" remodeling and counterexamples for weighted estimates with arbitrarily "smooth" weights

Spyridon Kakaroumpas, Sergei Treil

For an $A_p$ weight $w$ the norm of the Hilbert Transform in $L^p(w)$, $1<p<\infty$ is estimated by $[w{]}_{A_p}^s$, where $[w{]}_{A_p}$ is the $A_p$ characteristic of the weight $w$…