15 problems

Let $T$ be a Calderón–Zygmund operator, let $p>1$, and let $(u,v)$ be weights. Let $A$ and $B$ be Young functions, with $\bar A\in B_{p'}$ and $\bar B\in B_p$, and use the normaliz…

Consider the axially symmetric steady-state ansatz … with $l>-1$, $0<k<l+\frac{3}{2}$, and weighted norms involving … where $r(x)=\sqrt{x_1^2+x_2^2}$. Weighted-estimate conjecture.…

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 $2\leq m\leq n+1$ and let … For any $\varepsilon>0$, there exist constants $C_\varepsilon$ and $0<\delta_{\deg}\ll\delta\ll\varepsilon$ such that, for any $R\geq 1$, any…

Let $d\geq 1$ and let $\alpha\in(-1,\infty)$. Consider the corollary's hypotheses and conclusion for the boundary value problem in the half cylinder $Q_2^+$, with $p^*$ satisfying…

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…

Extra-bump avoidance conjecture. The terms involving $\gamma_{p,m}$ in the estimate for $T_b^m$ should be fully avoidable; equivalently, one should have

Parabolic Iwaniec conjecture. The optimal weighted estimate should be

Hytönen–Roncal–Tapiola conjecture. The quadratic dependence on $[w]_{A_2}$ in this estimate can be improved to linear dependence, namely an estimate of the form

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…

Pérez's conjecture. The estimate holds with $\Phi=\Psi$ for every weight $w$ and every $f\in L^1(M_{\Psi}w)$.

Let $\Omega$ be a bounded convex polygonal domain, let $r$ denote the radial weight variable, let $P$ be the Laplace-Leray projection, and let $u$ belong to a suitable space of fun…