18 problems

Positive boundedness conjecture. Every such datum $\mathbf{H}_\mathbf{M}$ is $\mathbf{p}$-bounded.

Let $\gamma(t)=(a_1t,a_2t,a_3t)$, where $a_1,a_2,a_3$ are nonzero and pairwise distinct, so that $\gamma$ is a nondegenerate line in $\mathbb{R}^3$. For $\vec f=(f_1,f_2,f_3)$ and…

Weak-type weighted Sobolev conjecture. For such $w$ and $f$,

For $d\geq2$, let $K_{\mathbb{H}^{(k)}}$ and $K_{R_\mathrm{dis}^{(k)}}$ be the kernels of the probabilistic and Calderón–Zygmund discrete Riesz transforms, respectively, with…

Let $\Omega$ be homogeneous of degree zero on $\mathbb{R}^d$, satisfy the vanishing moment condition, and let $A$ be a function on $\mathbb{R}^d$ whose derivatives of order one bel…

Let $b_1,b_2$ satisfy the same assumptions as in Theorems and. Let $H$ denote the Hilbert transform, let $A,B,C$ be Young functions, let $\bar A,\bar B,\bar C$ be their complementa…

Simplex Calderón–Zygmund form conjecture. Then

Stein's conjecture. The operator $H_{\Gamma}$ is bounded on $L^p(\mathbb{R}^2)$ for every $1<p<\infty$.

Let $\mathbb{W} \subset \mathbb{H}$ be a vertical subgroup with complementary subgroup $\mathbb{V}$, and let $\phi \colon \mathbb{W} \to \mathbb{V}$ be an intrinsic Lipschitz funct…

Let $T$ be a vector of standard singular integrals in higher dimensions, and suppose that $T$ is both strongly elliptic and strongly gradient elliptic. The energy conditions are th…

Let $b^{\alpha,n}$ denote an elliptic vector of standard $b$-fractional singular integrals in $b^n$, acting between weighted spaces $L^2(\mathbb{R}^n;\sigma)$ and…

Let $b^{\alpha,n}$ denote an elliptic vector of standard $b$-fractional singular integrals in $b^n$, and let $b$ and $b$ be weights. The notation $\mathcal{A}_2^\alpha$ denotes the…

Let $b$ and $b$ be weights on $b^n$, let $H$ be the Hilbert transform, and let $b_Q$ denote the two-tailed auxiliary function associated with a cube $Q$. Write $b_Q$ and $b_Q$ for…

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…

Multilinear Hilbert transform boundedness conjecture. For $k\geq 1$ and exponents $1<p_1,\dots,p_k,p<\infty$ satisfying $\frac{1}{p}=\frac{1}{p_1}+\dots+\frac{1}{p_k}$, the truncat…

Let $T_{\mathbf V}$ be the maximal directional singular integral associated with a finite set of $N$ directions ${\mathbf V}$, as defined in the source. Here $p'$ denotes the Hölde…

Let $\Gamma$ be a simple Carleson curve, let $w:\Gamma\to[0,\infty]$ be a weight, and let $p:\Gamma\to(1,\infty)$ be continuous and satisfy the Dini–Lipschitz condition. Let…