We study Hankel operators and commutators that are associated with a symbol and a kernel function. If the kernel function satisfies an upper bound condition, we obtain a sufficient condition for commutators to be bounded or compact. If the kernel function satisfies a local bound condition, the sufficient condition turns out to be necessary. The analytic and harmonic Bergman kernels satisfy both conditions, therefore a recent result by Wu on Hankel operators on harmonic Bergman spaces is extended.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-1-4,
author = {Jie Miao},
title = {Hankel type operators on the unit disk},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {55-68},
zbl = {0977.47021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-1-4}
}
Jie Miao. Hankel type operators on the unit disk. Studia Mathematica, Tome 147 (2001) pp. 55-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-1-4/