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

Joan Mateu·Joan Verdera
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Abstract

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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Joan Mateu, Joan Verdera. 2006-03-03. Lp and weak L1 estimates for the maximal Riesz transform and the maximal Beurling transform. https://arxiv.org/abs/math/0603077

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