L^p and weak L^1 estimates for the maximal Riesz transform and the maximal Beurling transform

We prove $L^p$ estimates for the maximal Riesz transform in terms of the Riesz transform itself, for $1<p \leq \infty$. We show that the corresponding weak~$L^1$~æestimate fails for the maximal Riesz transform, but surprisingly does hold for the maximal Beurling transform.

Full Text (PDF format)

Published 1 January 2006