3 problems

Let $Q\subset\mathbb{R}^d$ be a cube, let $\mathrm{BMO}_{\varepsilon}^{\mathrm{dyad}}(Q)$ denote the dyadic BMO class with parameter $\varepsilon$, and define … An extension…

Let $Q$ be a $d$-dimensional cube and let $f^*$ denote the monotone rearrangement of $f$ on $[0,1]$. Let $c(d)$ be the constant appearing in the dimension-reduction conjecture for…

Let ${\mathcal X}$ be the underlying space of homogeneous type, and let $BMO({\mathcal X})$, $H^1({\mathcal X})$, $L^1({\mathcal X})$, and $H^{\log}({\mathcal X})$ denote the space…