Stein (1956). As Charles Fefferman points out in his essay in Fefferman, Fefferman, Wainger (1995), the proof of Stein interpolation theorem is essentially that of the Riesz–Thorin theorem with the letter z added to the operator. To compensate for this, a stronger version of the Hadamard three-lines theorem, due to Isidore Isaac Hirschman, Jr., is used to establish the desired bounds. See Stein and Weiss (1971) for a detailed proof, and a blog post of Tao for a high-level exposition of the theorem.
