Mathematical Research Letters

Volume 13 (2006)

Number 6

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

Pages: 957 – 966

DOI: http://dx.doi.org/10.4310/MRL.2006.v13.n6.a10

Authors

Joan Mateu

Joan Verdera

Abstract

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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