8 problems

Let $E\subset\mathbb{R}^{n+1}$ be an Ahlfors–David regular set. The Riesz transform conjecture. Boundedness in $L^2(E)$ of the Riesz transform should imply that $E$ is uniformly re…

David–Mayboroda conjecture. Under these hypotheses, the Weak Geometric Lemma implies the Bilateral Weak Geometric Lemma, and consequently uniform rectifiability of $E$.

Let $E \subset \mathbb{R}^N$ be a closed Ahlfors-regular set. We say that $E$ has the property of projection if, for all $x \in E$ and all $0 < r < \operatorname{diam}(E)$, … where…

Necessity conjecture. If $\partial\Omega$ is not uniformly rectifiable, then the displayed bound holds for none of the weak DKP operators.

Let $\Omega \subset \mathbb{R}^{n+1}$ be an open set satisfying the corkscrew condition, with $n$-ADR boundary $\partial\Omega$. Suppose that extensions of boundary data exist with…

Let $\Omega\subset\mathbb{R}^{n+1}$ be an open set with uniformly rectifiable boundary. The weak local John condition means that there are constants $\lambda,\theta\in(0,1)$ and…

Let $\Gamma\subset\mathbb{R}^n$ be a uniformly rectifiable domain boundary of dimension $d$, and define … for some $\alpha>0$. Set $\mathfrak A(X)=D(X)^{-n+d+1}I$, where $I$ is the…

Converse conjecture. Converses to both the Carleson measure estimate and the $\varepsilon$-approximability theorem should hold, or perhaps a converse to their combination should ho…