Translator Disclaimer
Fall 2002 On the Schatten class membership of Hankel operators on the unit ball
Jingbo Xia
Illinois J. Math. 46(3): 913-928 (Fall 2002). DOI: 10.1215/ijm/1258130992

Abstract

A well-known theorem of K. Zhu \cite{6} asserts that, for $2 \leq p <\infty $, the Hankel operators $H_f$ and $H_{\bar f}$ on the Bergman space $L^2_a(B_n,dV)$ of the unit ball belong to the Schatten class ${\mathcal{C}}_p$ if and only if the mean oscillation $\MO(f)(z) = \{\widetilde{|f|^2}(z) - |\tilde f(z)|^2\}^{1/2}$ belongs to $L^p(B_n,(1-|z|^2)^{-n-1}dV(z))$. It is well known that, for trivial reasons, this theorem cannot be extended to the case $p \leq 2n/(n+1)$. This paper fills the gap between $2n/(n+1)$ and 2. More precisely, we prove that, when $2n/(n+1) < p < 2$, the same theorem holds true.

Citation

Download Citation

Jingbo Xia. "On the Schatten class membership of Hankel operators on the unit ball." Illinois J. Math. 46 (3) 913 - 928, Fall 2002. https://doi.org/10.1215/ijm/1258130992

Information

Published: Fall 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1042.47014
MathSciNet: MR1951248
Digital Object Identifier: 10.1215/ijm/1258130992

Subjects:
Primary: 47B35
Secondary: 32A70, 47B10, 47B32

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.46 • No. 3 • Fall 2002
Back to Top