6 problems

Let $\Gamma$ be a convex $C^2$ function on $[0,1]$, let $E_\Gamma$ be its extension operator, and let $\omega:B_R\to[0,\infty)$ be a one-dimensional weight, meaning … for every bal…

Let $B_R$ be the ball of radius $R$ centered at the origin, let $\mathbb{T}$ be the relevant family of tubes, and write $w(T)$ for the weight of a tube. Under the hypotheses of the…

Let $\Sigma\subset\mathbb{R}^d$ be a $C^2$ hypersurface with surface measure $\mathrm{d}\sigma$, let $f\in L^2(\Sigma;\mathrm{d}\sigma)$, and let $w$ be a nonnegative weight. Let…

Let $T$ be a non-degenerate Calderón–Zygmund operator with Dini-continuous kernel, let $m\in\mathbb N$ and $p>1$, and let $\lambda$, $\mu$, and $\eta$ be arbitrary weights. Here…

Let $B^m$ denote the $m$th operator in the family considered in the paper, and let $w\in A_2$ with classical $A_2$ characteristic $[w]_{A_2}$. Linear $A_2$ conjecture for $B^m$. Fo…

Let $T_{\Omega}$ be the rough homogeneous singular integral associated with an angular function $\Omega$, let $w\in A_2$ be a Muckenhoupt weight, and let $[w]_{A_2}$ denote its cla…