Let Ω be a piecewise smooth bounded convex Reinhardt domain in C2. Assume
that the symbols ϕ and ψ are continuous on \barΩ and harmonic on the disks
in the boundary of Ω. We show that if the product of Hankel operators H*ψ
Hϕ is compact on the Bergman space of Ω, then on any disk in the boundary of
Ω, either ϕ or ψ is holomorphic.