Abstract

We characterize boundedness and compactness of area operators from Hp into Lq(Sn) in terms of Carleson measures. Some of the tools used in the proof of the one dimensional case are not available in the higher dimension case, such as the strong factorization of Hardy spaces and the Calderón-Zygmund decomposition. Our approach involves a duality argument and maximal functions of Lp(Sn) functions in the unit ball of Cn.

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