11 problems

Nieraeth's conjecture. If $M$ is bounded on $X$, then $M$ is bounded on $X'$.

Let $X$ be a separable Banach function space over the unit circle, and let $H[X]$ be the corresponding abstract Hardy space. Denote by $P$ the Riesz projection and by…

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 $p_1,\ldots,p_m\in(1,\infty]$ with $\frac{1}{p}=\sum_{j=1}^m\frac{1}{p_j}>0$, and let $w=\prod_{j=1}^m w_j$. Suppose $T$ is well-defined on all $m$-tuples…

Let $T$ satisfy the full-range sparse domination bound referred to in the source. Let $X$ be a Banach function space such that $M:X\to X$ and $M:X'\to X'$ are bounded. Logarithmic…

Let $X$ be an $r$-convex and $s$-concave Banach function space over $\mega$ and suppose $\mathcal{E}$ has the $A_1$ self-improvement property. The conjecture. The following conditi…

Let $X( Omega)$ be a Banach function space, and let the difference quotient criterion be the condition in which the estimate referenced as equation DQC1:1 characterizes membership…

Convexity and concavity conjecture. These assumptions should be consequences of any of the conditions of Theorem 3.

Let $E$ be a Banach ideal space and let $\varphi$ and $\varphi_1$ be Orlicz functions. For a function space $E_{\varphi}$, write $M(E_{\varphi_1},E_{\varphi})$ for the space of poi…

Let $X$ be a Banach function space of locally integrable functions, so convergence in $X$ implies convergence in $L^1_{\mathrm{loc}}$, and suppose that $X$ is the dual of a Banach…