The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).
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