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## Studia Mathematica

2015 | 228 | 2 | 101-108
Tytuł artykułu

### Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes

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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 𝓢₂, 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 $p > (1- log π/log 4)^{-1}$ there exist multiplicative Hankel forms in the Schatten class $𝓢_{p}$ 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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101-108
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2015
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• Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
autor
• Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
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