8 problems

Let $C_p$ denote the constant in the Littlewood–Paley inequality referred to in the paper, for the relevant range of $p$. Pichorides' conjecture. One has … The optimal rate of grow…

Let $\Omega=\{\omega_j\colon j\in\mathbb Z\}$ be a collection of intervals that partitions $\mathbb R$, and let $\operatorname S^\Omega$ denote the associated square function. Supp…

Let $1\leq p,s<\infty$. For some $\mu>0$, let $C_\mu$ be a constant such that, for every $j\geq1$ and every sequence $\{f_k\}$ satisfying…

$L^p$-boundedness conjecture. The function $\widetilde{H}$ should resolve the issue of $L^p$-unboundedness: unlike $\widetilde{G}$ for $p>2$ and $H$ for $1<p<2$, it is expected to…

Let $\{T_t\}_{t>0}$ be the heat semigroup generated by a Schrödinger operator as above, and let $\{P_t\}_{t>0}$ be the Poisson semigroup subordinated to $\{T_t\}_{t>0}$. Let $X$ be…

Let $p\in(1,\,\infty)$, let $\lambda\in(3,\,\infty)$, let $\varphi\in C^\infty(\mathbb{R}^n)$ be supported in $\{x\in\mathbb{R}^n:|x|\leq 1\}$ with…

Let $\omega$ be a radial weight, let $0<p<\infty$, and let $k\in\mathbb{N}$. For a holomorphic function $f\in\mathcal{H}(\mathbb{D})$, write $A^p_\omega$ for the corresponding weig…

Let $w$ be a weight on ${\mathbb R}^n$, let $1<p<\infty$, and define its $A_p$ characteristic by … where the supremum is over cubes $Q\subset {\mathbb R}^n$. Let $S$ be a Littlewoo…