Lp and weak L1 estimates for the maximal Riesz transform and the maximal Beurling transform

Details Lp and weak L1 estimates for the maximal Riesz transform and the maximal Beurling transform Lp and weak L1 estimates for the maximal Riesz transform and the maximal Beurling transform

2006-03-03

arxiv.org/abs/math/0603077v1

Math. Res. Lett. 13 (2006), no. 5-6, 957-966

Mathematics

Classical Analysis and ODEs

12 pages

Scientific paper

We estimate in Lp the maximal Riesz transform in terms of the Riesz transform
itself for p greater than 1. In the limiting case p=1 the weak L1 inequality is
shown to fail. Surprisingly, the weak L1 inequality for the maximal Beurling
transform in terms of the Beurling transform does hold.

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