Cyclic vectors in 𝐴^{-∞}

Abstract

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