Compactness of products of Hankel operators on convex Reinhardt domains in C2

摘要

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