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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We study the reproducing kernel Hilbert space with kernel kd , where d is a positive integer and k is the reproducing kernel of the analytic Dirichlet space.
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