Conditional square functions, the sine-cosine decomposition for Hardy martingales and dyadic perturbation
Volume 167 / 2022
Colloquium Mathematicum 167 (2022), 329-340
MSC: Primary 60G42; Secondary 60G46, 32A35.
DOI: 10.4064/cm8117-1-2021
Published online: 9 August 2021
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 $L^1/H^1$.
