16 problems

Let $w\in A_1$ be a weight, with … and let $T$ be a Calderón–Zygmund operator. Weak Muckenhoupt–Wheeden conjecture. The weak-type estimate … should hold with linear dependence on…

Let $w$ be a weight and define … Set $\sigma=w^{1-p'}$, where $1<p<\infty$, and let $T$ be a Calderón–Zygmund operator. Lacey's mixed $A_p$–$A_\infty$ conjecture. The estimate … sh…

Let $w\in A_\infty$, and denote its $A_\infty$ characteristic by $[w]_{A_\infty}$. For dimensional constants $C_n>0$, consider the embedding of $A_\infty$ into an $A_p$ class, wher…

Let $1<p\leq q<\infty$, let $w$ be a weight, and let $M$ denote the Hardy–Littlewood maximal operator. Let $T$ range over all Calderón–Zygmund operators and let $R_j$,…

Morrey–block duality conjecture. If

Let $\phi$ be a generalized $\Phi$-function, let $\phi^*$ be its complementary function, and define … Assume that $\phi^*$ satisfies the $\Delta_2$ condition and that $\phi$ satisf…

Let $\phi$ be a generalized $\Phi$-function, let $\phi^*$ be its complementary generalized $\Phi$-function, and let $M$ denote the Hardy–Littlewood maximal operator. Assume that bo…

Let $p:{\mathbf R}^d\to[1,\infty]$ satisfy $1<p_-\leq p_+<\infty$, let $w$ be a weight, and let $A_{\mathrm{FW}}$ and $A_{\mathrm{strong}}$ denote the relevant Muckenhoupt-type con…

Let $M$ denote the Hardy–Littlewood maximal operator, let $X$ be a Banach function space, and let $X'$ be its Köthe associate space. Assume that $1<s<\infty$ and that $X$ is $s$-co…

Let $M$ denote the Hardy–Littlewood maximal operator, let $X$ be a Banach function space, and let $X'$ be its Köthe associate space. For $1<r\leq s<\infty$, assume that $X$ is $r$-…

Let $1<p<\infty$, let $\varphi_p$ be the extremal function, and let $\mathscr{Z}(\varphi_p)$ be its zero set. Write $\operatorname{dist}(x,\mathscr{Z}(\varphi_p)\cup\{0\})$ for the…

Parabolic Iwaniec conjecture. The optimal weighted estimate should be

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 $1<p<\infty$ and let $W=(w_{ij})\colon \mathbb{R}^n\times \mathbb{R}^m\to\mathbb{C}^{N\times N}$ be a matrix weight in the set of Muckenhoupt weights…

Let $w\in A_1$ be a weight, with … and let $T$ be a Calderón–Zygmund operator. $L\log L$ sharpness conjecture. The logarithmic dependence in … is best possible as a function of…

Let $1\leq p\leq\infty$ and let $\{\omega^t\}_{t\in[0,1]}$ be a family of dyadic $A_p$ weights. Define its translation-average by … Assume that $\omega$ is doubling. Doubling trans…