6 problems

The remainder characterization conjecture. The sequence ${\mathbf A}$ is a $\mathrm{TP}_\infty$-preserver if and only if, for every $l\in\mathbb N\cup\{0\}$, $R_l[\mathbf A]$ is an…

Let $n\ge 2$. For $1 \le p \le \frac{2n}{n-1}$, consider the convolution operator … where $B_1$ is the unit ball in $\mathbb{R}^n$. Injectivity conjecture. The convolution operator…

Let $G$ be a locally compact group, and let $p\in(1,\infty)$ with $p\neq 2$. Denote by $PM_p(G)$ the algebra of $p$-pseudomeasures and by $CV_p(G)$ the algebra of $p$-convolution o…

Let $\phi$ be an entire function of exponential type, and let $D$ denote differentiation on the space of entire functions. The convolution operator $\phi(D)$ is defined by the symb…

Let $G$ be a compact locally compact group, and let $T$ be a convolution operator on $G$. For $1<p<2$, suppose that $T$ is bounded on the weak Lebesgue space $L^{p,infty}(G)$. Pisi…

Let $G$ be a locally compact abelian group, and let $X$ be a space of locally integrable functions on $G$ whose norm is shift-invariant. For $\mu\in M(G)$, where $M(G)$ is the alge…