Accepted article
Published 2024-02-06
Keywords
- Hilbert transform,
- distribution function,
- decreasing rearregement,
- Hardy's inequality
How to Cite
Chaparro, H. C., & Castillo, R. E. (2024). Boundedness of the Hilbert Transform on Rearrangement Invariant Spaces. Revista Integración, Temas De matemáticas, 42(1), 1–21. https://doi.org/10.18273/revint.v42n1-2024001
Copyright (c) 2024 Revista Integración, temas de matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
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 $L_{p}$-boundedness of the Hilbert transform. This is a celebrated theorem due to M. Riesz.
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