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Martingale Transforms and Complex Uniform Convexity
Martingale transforms and Calderon-Zygmund singular integral operators are bounded as operators from ${L_2}({L_1})$ to ${L_2}({L_q})$ when $0 < q < 1$. If $Y$ is a reflexive subspace of ${L_1}$ then ${L_1}/Y$ can be renormed to be $2$-complex uniformly convex. A new proof of the cotype 2 property of ${L_1}/{H_1}$ is …