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<p>We define and study the fractional Stockwell transform (FRST) for fractional Lizorkin distributions. Within this distributional framework, we establish the Parseval identity — also referred to as the desingularization formula — and characterize bounded subsets of fractional Lizorkin space of distributions. Furthermore, a number of Abelian and Tauberian theorems yield a complete characterization of the quasiasymptotic behavior of distributions at the origin and infinity in terms of the asymptotic behavior of their FRST.</p>

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Tauberian theorems for the fractional Stockwell transform of Lizorkin distributions

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Astrit Ferizi,
  • Katerina Hadzi-Velkova Saneva

摘要

We define and study the fractional Stockwell transform (FRST) for fractional Lizorkin distributions. Within this distributional framework, we establish the Parseval identity — also referred to as the desingularization formula — and characterize bounded subsets of fractional Lizorkin space of distributions. Furthermore, a number of Abelian and Tauberian theorems yield a complete characterization of the quasiasymptotic behavior of distributions at the origin and infinity in terms of the asymptotic behavior of their FRST.