Advances in Harmonic Analysis

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 459

Special Issue Editor


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Guest Editor
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Interests: classical harmonic analysis; harmonic analysis on groups; harmonic analysis techniques to PDE; functions spaces
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Special Issue Information

Dear Colleagues,

Harmonic analysis is one of the core areas of modern analytical mathematics. Over the centuries, it has formed an extensive subject system and has important and profound applications in the fields of mathematics, as well as other related fields.

This Special Issue, entitled “Advances in Harmonic Analysis”, is devoted to collecting research papers of higher quality on the recent progress in harmonic analysis, as well as some applications in various fields of mathematics, such as partial differential equations, probability, and geometry. We would like to invite original research articles that provide new results in this subject. All topics on harmonic analysis and related applications are welcome, in particular, the theory of linear and multilinear Calderón-Zygmund operators, real analysis and abstract analysis, etc.

Potential topics can be related to, but are not limited to, the keywords listed below. 

  • linear Calderón–Zygmund operators;
  • multilinear Calderón–Zygmund operators;
  • smoothness and function spaces;
  • square functions;
  • Fourier analysis;
  • Hardy–Littlewood maximal functions;
  • compactness;
  • weighted norm inequalities;
  • interpolation theory;
  • convolution operators;
  • non-convolution operators;
  • Littlewood–Paley theory

I look forward to receiving your contributions.

Prof. Dr. Qingying Xue
Guest Editor

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Keywords

  • linear Calderón–Zygmund operators
  • multilinear Calderón–Zygmund operators
  • smoothness and function spaces
  • square functions
  • Fourier analysis
  • Hardy–Littlewood maximal functions
  • compactness
  • weighted norm inequalities
  • interpolation theory
  • convolution operators

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Published Papers (1 paper)

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Research

32 pages, 380 KiB  
Article
Localization Operators for the Linear Canonical Dunkl Windowed Transformation
by Saifallah Ghobber and Hatem Mejjaoli
Axioms 2025, 14(4), 262; https://doi.org/10.3390/axioms14040262 - 30 Mar 2025
Viewed by 217
Abstract
One of the best known time–frequency tools for examining non-transient signals is the linear canonical windowed transform, which has been used extensively in signal processing and related domains. In this paper, by involving the harmonic analysis for the linear canonical Dunkl transform, we [...] Read more.
One of the best known time–frequency tools for examining non-transient signals is the linear canonical windowed transform, which has been used extensively in signal processing and related domains. In this paper, by involving the harmonic analysis for the linear canonical Dunkl transform, we introduce and then study the linear canonical Dunkl windowed transform (LCDWT). Given that localization operators are both theoretically and practically relevant, we will focus in this paper on a number of time–frequency analysis topics for the LCDWT, such as the Lp boundedness and compactness of localization operators for the LCWGT. Then, we study their trace class characterization and show that they are in the Schatten–von Neumann classes. Then, we study their spectral properties in order to give some results on the spectrograms for the LCDWT. Full article
(This article belongs to the Special Issue Advances in Harmonic Analysis)
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