Mathematical Research Letters
Volume 13 (2006)
L^p and weak L^1 estimates for the maximal Riesz transform and the maximal Beurling transform
Pages: 957 – 966
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.
Published 1 January 2006