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

Abstract

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

8 pages