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Title: A lower bound in Nehari's theorem on the polydisc
Author: Ortega Cerdà, Joaquim
Seip, Kristian
Keywords: Teoria d'operadors
Anàlisi de Fourier
Anàlisi harmònica
Funcions de diverses variables complexes
Operator theory
Fourier analysis
Harmonic analysis
Functions of several complex variables
Issue Date: Oct-2012
Publisher: Springer
Abstract: By theorems of Ferguson and Lacey ($d=2$) and Lacey and Terwilleger ($d>2$), Nehari's theorem is known to hold on the polydisc $\D^d$ for $d>1$, i.e., if $H_\psi$ is a bounded Hankel form on $H^2(\D^d)$ with analytic symbol $\psi$, then there is a function $\varphi$ in $L^\infty(\T^d)$ such that $\psi$ is the Riesz projection of $\varphi$. A method proposed in Helson's last paper is used to show that the constant $C_d$ in the estimate $\|\varphi\|_\infty\le C_d \|H_\psi\|$ grows at least exponentially with $d$; it follows that there is no analogue of Nehari's theorem on the infinite-dimensional polydisc.
Note: Versió postprint del document publicat a:
It is part of: Journal d'Analyse Mathematique, 2012, vol. 118, num. 1, p. 339-342
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ISSN: 0021-7670
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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