Products of Hankel operators on the Fock space

Abstract

For entire functions f and g we study the problem of when the Hankel product Hf‾⁎Hg‾ is bounded or compact on the Fock space Fα2. This is a companion to Sarason's Toeplitz product problem which was completely solved for the Fock space by Cho–Park–Zhu in 2014. Surprisingly, our results here are different from the natural conjectures motivated by the Toeplitz product problem.