3 problems

The paper considers commutator operators built from paraproducts, including iterated operators such as $C(f,g,h)=(f\prec g)\circ h-f(g\circ h)$ and related higher-order expressions…

Kato–Ponce fractional commutator conjecture. For $s>0$, the term $\|J^s f\|_p\|g\|_\infty$ on the right-hand side can be replaced by $\|J^{s-1}\partial f\|_p\|g\|_\infty$, yielding

Let $H$ and $A$ belong to a $C^{*}$-algebra, with $H$ a positive contraction satisfying $0\leq H\leq1$ and $\left\Vert A\right\Vert\leq1$. For the square-root function…