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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.fatcat:aieeyvzhynffjhmc3xwn5nie2e