Bounded Hankel products on Fock-Sobolev spaces

Let $F^{2,m}$ denote the Fock-Sobolev space of complex plane. The purpose of this paper is to study the conjecture which was shown to be false for Fock space by Ma-Yan-Zheng-Zhu in 2019. For the certain symbol space, the main result of the paper says that the conjecture is actually true in $F^{2,m}$ if $m$ is a positive integer.