Sharp mutliplicative inequalities with $\mathrm{BMO}$ $\mathrm{I}$

Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy

We find the best possible constant $C$ in the inequality $\Vert \phi {\Vert }_{L^r}\le C\Vert \phi {\Vert }_{L^p}^{\frac{p}{r}}\Vert \phi {\Vert }_{\mathrm{BMO}}^{1-\frac{p}{r}}$, where $2\le r$ and $p<r$. We employ t…