Compact Hankel operators on the Bergman space

Abstract

Let D { z C" zl < 1} denote the open unit disk in the complex plane C, and let A denote the usual Lebesgue area measure on C. For 1 < p < oo and f: D --, C Lebesgue measurable let Ilfllp (/Dill Dr)X/P. The Bergman space L[(D) is the Banach space of analytic functions f: D --, C such that [Ifl[, < oo. The Bergman space L2(D) is a Hilbert space; it is a dosed subspace of the Hilbert space L2(D, dA/r) with inner product given by g> f (z)g(z)