7 problems

Dimension-free Cauchy-transform conjecture. For every $w\in A_2$ and the Cauchy transform $C$ in $\mathbb C^n$, the displayed estimate holds with an implied constant independent of…

Sharp $A_2$ exponent conjecture. The best possible power of $Q_2(w)$ in such a weighted operator bound is $1$.

Treil's matrix $A_2$ conjecture. The matrix $A_2$ condition is necessary and sufficient for the boundedness of the Hilbert transform on the corresponding weighted vector-valued…

Let the disc multiplier be the Fourier multiplier on $\mathbb{R}^d$ whose symbol is the indicator function of a Euclidean ball. A weighted inequality of the general form … should h…

Let $T$ be a Calderón–Zygmund operator, let $1<p<\infty$, and let $w$ be an $A_p$ weight, with … Here $\|T\|_{L^p(w)}$ denotes the operator norm on the weighted space $L^p(w)$. The…

Let $w$ be an $A_1$ weight, let $[w]_{A_1}$ denote its $A_1$ norm, and let $H$ be the Hilbert transform. The $A_1$ conjecture. The operator $H$ should map $L^1(w)$ to…

Let $W$ be a $d\times d$ matrix weight in $A_2$, and let $S_W$ denote the associated square function on $L^2(W)$. Matrix weighted square function conjecture. … The scalar analogue…