Hankel type operators on the unit disk

We study Hankel operators and commutators that are associated with a symbol and a kernel function. If the kernel function satisfies an upper bound con dition, we obtain a sufficient condition for commutators to be bounded or c ompact. If the kernel function satisfies a local bound condition, the suffi cient condition turns out to be necessary. The analytic and harmonic Bergma n kernels satisfy both conditions, therefore a recent result by Wu on Hanke l operators on harmonic Bergman spaces is extended.