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arXiv · 1409.3117

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

Ole Fredrik Brevig·Karl-Mikael Perfekt
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Abstract

Ortega-Cerdà -- Seip demonstrated that there are bounded multiplicative Hankel forms which do not arise from bounded symbols. On the other hand, when such a form is in the Hilbert-Schmidt class $\mathcal{S}_2$, Helson showed that it has a bounded symbol. The present work investigates forms belonging to the Schatten classes between these two cases. It is shown that for every $p>(1-\logπ/\log{4})^{-1}$ there exist multiplicative Hankel forms in the Schatten class $\mathcal{S}_p$ which lack bounded symbols. The lower bound on $p$ is in a certain sense optimal when the symbol of the multiplicative Hankel form is a product of homogeneous linear polynomials.

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Ole Fredrik Brevig, Karl-Mikael Perfekt. 2015-09-07. Failure of Nehari's Theorem for Multiplicative Hankel Forms in Schatten Classes. https://doi.org/10.4064/sm228-2-1

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