20210802 鲍官龙 Littlewood-Paley estimates for weighted Bergman spaces

$$\int_\mathbb{D} |f(z)|^p \omega(z) dA(z)<\infty$$

if and only if

$$\int_\mathbb{D} |f'(z)|^p (1-|z|^2)^p \omega(z) dA(z)<\infty,$$

where $f$ is analytic in $\mathbb{D}$ and $dA$ is the area measure on $\mathbb{D}$.  A complete solution to this problem is still lacking. We will talk about  some  results   and  applications of these Littlewood-Paley estimates.