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/