Bi‐commutators of fractional integrals on product spaces

Recently Lacey extended Chanillo's boundedness result of commutators with fractional integrals to a higher parameter setting. In this paper, we extend Lacey's result to higher dimensional spaces by a different method. Our method is in terms of the dual relationship between product BMO and product Hardy space and the maximal function characterization of product Hardy spaces obtained by S.-Y.Chang and R. Fefferman. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)