It is known that Beurling's theorem concerning invariant subspaces is not true in the Bergman space (in contrast to the Hardy space case). However, Aleman, Richter, and Sundberg proved that every cyclic invariant subspace in the Bergman space \lpad, 0
"A Beurling-type theorem in Bergman spaces,"
Turkish Journal of Mathematics: Vol. 35:
4, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss4/11