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 $\Ha_ϕ$ 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 $p>(1-\log \pi /\log 4{)}^{-1}=\mathrm{5.7388...}$.

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