2 problems

Continuity conjecture. If $\mathscr{M}$ is a $\textbf1$-Hardy mean, then its weighted Hardy constant $\mathscr{H}_{\mathscr{M}}$ is continuous in the pointwise topology.

Let $p,q\in\mathbb{R}$, and define the Gini mean by … The preceding proposition shows that if $\mathfrak{G}_{p,q}$ is a Hardy mean, then $\min(p,q)\leq 0$ and $\max(p,q)\leq 1$, wh…