4 problems

Least-atom principle. For all $1<p<q<\infty$,

Critical-extremizer characterization.

For $2\leq p<8$, let $t'_p$ denote the optimal time and let $\beta$ be the parameter of the quantum Ornstein–Uhlenbeck semigroup. There are positive constants…

Let $n\geq 1$ and $t\geq 0$, let $\mu_t=\frac{1-e^{-t}}{2}\delta_{-1}+\frac{1+e^{-t}}{2}\delta_1$, and let $\mu=\mu_\infty$ be the uniform probability measure on $\{-1,1\}$. Write…