Failure of Nehari's Theorem for Multiplicative Hankel Forms in Schatten Classes II

Abstract

We prove that for any $p>4$ we can find a Schatten class Hankel operator $\Ha_\phi$ defined on the Hardy space of the infinite torus $H^2(\mathbb{T}^\infty)$ that belongs to the Schatten class $S^p$ but does not admit a bounded symbol, extending the previously known range $p>(1-\log\pi /\log 4)^{-1}=5.7388...$.