This paper completely characterizes the commuting problem of two small Hankel operators acting on the harmonic Bergman space with the symbols one being bounded and another being quasihomogeneous, or both being harmonic. The characterizations for semi-commuting problem and the product of two small Hankel operators being another small Hankel operator for certain class of symbols are also obtained.
"Algebraic properties of small Hankel operators on the harmonic Bergman space." Illinois J. Math. 59 (2) 295 - 317, Summer 2015. https://doi.org/10.1215/ijm/1462450702