Cyclic vectors in $A^{-\infty }$

Abstract:

If $f$ is in ${A^{ - p}}$, then $f$ is cyclic in ${A^{ - \infty }}$ if and only if $f$ is cyclic in every ${A^{ - q}}(q{\text { > }}p)$. An analogous result holds for the Bergman spaces ${B^p}$. In this note we apply the theory developed in [2 and 3] to explain the relationship between cyclic vectors in ${A^{ - \infty }}$ and ${A^{ - p}}$ or ${B^p}$.