A question of Toeplitz operators on the harmonic Bergman space (Q2427771)

If an analytic and a co-analytic Toeplitz operator on harmonic Bergman space commute, \textit{B. R. Choe} and \textit{Y. J. Lee} [Mich.\ Math.\ J.\ 46, No.~1, 163--174 (1999; Zbl 0969.47023)] posed the question whether then one of their symbols must be constant. The author shows that the answer is yes if one of their symbols is bounded.