Finite rank products of Toeplitz operators on the harmonic Bergman space (Q627372)

The harmonic Bergman space is the set of all complex-valued harmonic functions \(f\) on the open unit ball in \(\mathbb R^n\) (\(n\geq2\)) such that \[ \| f \|_{2}= \left\{\int_B|f|^{2}\,dV \right\}^{1/2}<\infty. \] It is shown that, if the product of Toeplitz operators with harmonic symbols having some boundary smoothness has finite rank, then one of the symbols is identically zero.