Conditional Square Functions, the Sine-Cosine Decomposition for Hardy Martingales and Dyadic Perturbation

We prove that the $\cal P$ norm estimate between a Hardy martingale and its cosine part are stable under dyadic perturbations, and show how dyadic stability of the $\cal P$ norm estimate is used in the proof that $L^1$ embeds into $L^1/H^1$.

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