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Martingale transforms and Calderon-Zygmund singular integral operators are bounded as operators from L2 (Ld to L2 (Lq) when 0 < q < 1. If Y is a reflexive subspace of LI then L,IY can be renormed to be 2-complex uniformly convex. A new proof of the co type 2 property of L,I H, is given.doi:10.1090/s0002-9947-1986-0825718-5 fatcat:veqdql7ahbbmjphtckfwfvhnya