The contractive divisor property for Bergman spaces states
that
given a non-zero square-integrable holomorphic function f on the disc,
there exists a holomorphic function g such that f/g is holomorphic,
nowhere zero, and has square integral no greater than that of f. Recent
work by Aleman, Richter, and McCullough establishes this result via a
reproducing kernel approach. I will discuss the relevant articles.