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....

In an earlier paper, the first two authors have shown that the convolution of a function $f$ continuous on the closure of a Cartan domain and a $K$-invariant finite measure $\mu$ on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face $F$ depends only on the restriction of $f$ to $F$ and is equal to the convolution, in $F$, of the latter restriction with some measure ${\mu }_F$ on $F$ uniquely determined by $\mu$. In this article, we give an explicit formula for ${\mu }_F$ in terms of $F$,...