Abstract

CASTILLO, René Erlin  and  CHAPARRO, Héctor Camilo. Boundedness of the Hilbert Transform on Rearrangement Invariant Spaces. Integración - UIS [online]. 2024, vol.42, n.1, pp.1-21.  Epub Jan 01, 2024. ISSN 0120-419X.  https://doi.org/10.18273/revint.v42n1-2024001.

In this self-contained review, the aspects about the applications of decreasing rearrangement techniques to the analysis of pointwise estimates for the Hilbert transform are analyzed. We make a consistent revision of these techniques in the proof of the Lp-boundedness of the Hilbert transform. This is a celebrated theorem due to M. Riesz.

Keywords : Hilbert transform; distribution function; decreasing rearregement; Hardy’s inequality.

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