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The purpose of this paper is to extend an interpolation theorem for sublinear operators on Lp spaces, obtained by Calderon and Zygmund, to similar operators acting on Hp spaces, p >0 [I]. We begin by making a few definitions. Let T be a mapping defined on a class of functions that are analytic in the interior of the unit circle I w| 0, if the domain of T includes Ha and there exists a constant M, independent of F in Ha, such that jjTFjjb <M ||Fjja (the norm on the left is the Lb norm and the norm on the right is the Ha norm). For the results in the theory of Hp spaces we shall use, we refer the reader to [2 ].

An interpolation theorem for sublinear operators on 𝐻_{𝑝} spaces