4 problems

Let $\phi$ be a generalized $\Phi$-function, let $\phi^*$ be its complementary function, and define … Assume that $\phi^*$ satisfies the $\Delta_2$ condition and that $\phi$ satisf…

Let $\phi$ be a generalized $\Phi$-function, let $\phi^*$ be its complementary generalized $\Phi$-function, and let $M$ denote the Hardy–Littlewood maximal operator. Assume that bo…

The UMD$^-_{\rm PW}$ conjecture. If $\Phi\in\Delta_2$, then $L^{\Phi}(T)$ is UMD$^-_{\rm PW}$.

Let $p\funccolon\mathbb{R}^n\to\mathbb{R}$ satisfy the log-Hölder continuity condition, with $p^-\in(1,\infty)$, and let $\{\psi_\epsilon\}_{\epsilon>0}$ be a family of functions a…