Commutators and Related Operators on Harmonic Bergman Space of Rn+1+

We study commutators and related operators on harmonic Bergman space—theL2(Rn+1+) closure of the null space of Laplacian. By decomposingL2(Rn+1+) into the sum of null spaces of powers of Laplacian, and using the theory of paracommutators studied in [JP], we characterize harmonic symbols for which the associated commutators are bounded or compact. Operators associated to the Div–Curl theorem (in [CLMS]) in the theory of compensated compactness are also characterized.