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 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 there exist multiplicative Hankel forms in the Schatten class 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-2-1,
author = {Ole Fredrik Brevig and Karl-Mikael Perfekt},
title = {Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {101-108},
zbl = {1328.47027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-2-1}
}
Ole Fredrik Brevig; Karl-Mikael Perfekt. Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes. Studia Mathematica, Tome 231 (2015) pp. 101-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-2-1/