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<p>In this expository paper, we present a&#xa0;self-contained derivation of the Hilbert transform for periodic functions and revisit established results concerning its global behavior, particularly its strong boundedness in <i>L</i><sub><i>p</i></sub> spaces. We follow a&#xa0;novel perspective that relies on basic real analysis concepts, introduced in [<CitationRef CitationID="CR21">21</CitationRef>].</p>

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Revisiting the hilbert transform of periodic functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月25日

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  • René E. Castillo,
  • Edixon M. Rojas

摘要

In this expository paper, we present a self-contained derivation of the Hilbert transform for periodic functions and revisit established results concerning its global behavior, particularly its strong boundedness in Lp spaces. We follow a novel perspective that relies on basic real analysis concepts, introduced in [21].