Bounded Hankel products on Fock-Sobolev spaces

TL;DR

This paper investigates a conjecture related to bounded Hankel products on Fock-Sobolev spaces, demonstrating that it holds true for positive integer orders, contrasting previous results on Fock spaces.

Contribution

It proves that a conjecture about bounded Hankel products, false for Fock spaces, is true for Fock-Sobolev spaces when the order is a positive integer.

Findings

Conjecture is true in Fock-Sobolev spaces for positive integer m

Contrasts with previous false results for Fock spaces

Provides new insights into Hankel operators on Fock-Sobolev spaces

Abstract

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.