Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 42 No. 1 (2024): Revista Integración, temas de matemáticas
Research and Innovation Articles

Boundedness of the Hilbert Transform on Rearrangement Invariant Spaces

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Héctor Camilo Chaparro
Universidad de Cartagena
René Erlin Castillo
Universidad Nacional de Colombia
DOI: https://doi.org/10.18273/revint.v42n1-2024001

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

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Creative Commons License

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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