Compactness of products of Hankel operators on convex Reinhardt domains in C

Zeljkočučkovi´c, Zeljkoˇ Zeljkočučkovi´, Zeljkočučkovi´c, Sönmez ¸ahuto˘ Glu
Let Ω be a piecewise smooth bounded convex Reinhardt domain in C 2. Assume that the symbols φ and ψ are continuous on Ω and harmonic on the disks in the boundary of Ω. We show that if the product of Hankel operators H * ψ H φ is compact on the Bergman space of Ω, then on any disk in the boundary of Ω, either φ or ψ is holomorphic.