Mathematical Research Letters

Volume 13, Issue 6, November 2006 pp. 957-966.

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

Authors: Joan Mateu (1) and Joan Verdera (2)
Author institution: Universitat Autònoma de Barcelona

Summary: 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.

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