Sequences of zeroes of holomorphic functions in weight spaces in the unit disk

Let $\mathbb D$ be the unit disk in the complex plane $\mathbb C$ and let $H$ be a certain weight class of holomorphic functions in $\mathbb D$. We establish conditions under which a given sequence of points $\Lambda=\{\lambda_k\}_{k=1}^\infty\subset\mathbb D$ is the sequence of zeroes of a function from $H$.