We give a div -curl type lemma for the wedge product of closed differential forms on R n when they have coefficients respectively in a Hardy space and L ∞ or a space of BM O type. In this last case, the wedge product belongs to an appropriate Hardy-Orlicz space.1991 Mathematics Subject Classification. 42B30 (58A10).

We define as a distribution the product of a function (or distribution) h in some Hardy space H p with a function b in the dual space of H p . Moreover, we prove that the product b × h may be written as the sum of an integrable function with a distribution that belongs to some Hardy-Orlicz space, or to the same Hardy space H p , depending on the values of p.

We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function spaces.

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Abstract. We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley g * λ -function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by BM O functions are also considered.