7 problems

Let $LM^{p,r;\kappa}(\mathbb R^n)$ denote the Lorentz–Morrey space, and let $M^{p;\kappa}(\mathbb R^n)$ and $\operatorname{BMO}(\mathbb R^n)$ be the Morrey and bounded mean oscilla…

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 $n\in{\mathbb N}$, $-n<\varrho<0$, $s\in{\mathbb R}$, and $0<p<\infty$, $0<q\leq\infty$. Let ${\varrho}$-$B^s_{p,q}({\mathbb R}^n)$ denote either…

Let $-n<\varrho<0$, $0<p<\infty$, and $0<q\leq\infty$. Consider the spaces ${\Lambda}_{\varrho}B^s_{p,q}({\mathbb R}^n)$ and ${\Lambda}^{\varrho}B^s_{p,q}({\mathbb R}^n)$, and let…

Let $n\in {\mathbb N}$, $-n<\varrho<0$, and $s,s_1,s_2\in{\mathbb R}$. Let $0<p,p_1,p_2<\infty$ and $0<q,q_1,q_2\leq\infty$. Coincidence conjecture. Part (i) of Theorem should rema…

Lorentz-Morrey Riesz-potential conjecture. If $p_1$ and $q_1$ satisfy