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Mathematics
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Recent Advances in Harmonic Analysis and Applications
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Recent Advances in Harmonic Analysis and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 10395

Special Issue Editor

Prof. Dr. Qingying Xue

E-Mail Website
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
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Harmonic analysis is one of the core areas of modern analytical mathematics. Over the centuries, it has formed a huge subject system and has important and profound applications in the fields of mathematics, information processing, probability, and quantum mechanics.

This Special Issue, entitled “Recent Advances in Harmonic Analysis and Applications”, is devoted to collecting research papers 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 in harmonic analysis and related applications are welcome, in particular, the theory of linear and multilinear Calder\'{o}n-Zygmund operators, real analysis and abstract analysis, etc. Potential topics can be related to, but are not limited to, the keywords listed below. 

Prof. Dr. Qingying Xue
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • linear Calderón-Zygmund operators
  • multilinear Calderón-Zygmund operators
  • smoothness and function spaces
  • square functions
  • fourier analysis
  • hardy–littlewood maximal functions
  • compactness
  • weighted inequalities
  • boundedness
  • interpolation
  • convolution operators
  • non-convolution operators
  • littlewood–paley theory

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Published Papers (5 papers)

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Research

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14 pages, 309 KiB  
Article
On the Commutators of Marcinkiewicz Integral with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces
by Fuli Ku and Huoxiong Wu
Mathematics 2022, 10(11), 1817; https://doi.org/10.3390/math10111817 - 25 May 2022
Cited by 2 | Viewed by 2027
Abstract
This paper is devoted to exploring the mapping properties for the commutator μΩ,b generated by Marcinkiewicz integral μΩ with a locally integrable function b in the generalized Campanato spaces on the generalized Morrey spaces. Under the assumption that the [...] Read more.
This paper is devoted to exploring the mapping properties for the commutator μΩ,b generated by Marcinkiewicz integral μΩ with a locally integrable function b in the generalized Campanato spaces on the generalized Morrey spaces. Under the assumption that the integral kernel Ω satisfies certain log-type regularity, it is shown that μΩ,b is bounded on the generalized Morrey spaces with variable growth condition, provided that b is a function in generalized Campanato spaces, which contain the BMO(Rn) and the Lipschitz spaces Lipα(Rn) (0<α≤1) as special examples. Some previous results are essentially improved and generalized. Full article
(This article belongs to the Special Issue Recent Advances in Harmonic Analysis and Applications)
22 pages, 363 KiB  
Article
Boundedness of the Vector-Valued Intrinsic Square Functions on Variable Exponents Herz Spaces
by Omer Abdalrhman Omer and Muhammad Zainul Abidin
Mathematics 2022, 10(7), 1168; https://doi.org/10.3390/math10071168 - 3 Apr 2022
Cited by 3 | Viewed by 1590
Abstract
In this article, the authors study the boundedness of the vector-valued inequality for the intrinsic square function and the boundedness of the scalar-valued intrinsic square function on variable exponents Herz spaces [...] Read more.
In this article, the authors study the boundedness of the vector-valued inequality for the intrinsic square function and the boundedness of the scalar-valued intrinsic square function on variable exponents Herz spaces K˙ρ(·)α,q(·)(Rn). In addition, the boundedness of commutators generated by the scalar-valued intrinsic square function and BMO class is also studied on K˙ρ(·)α,q(·)(Rn). Full article
(This article belongs to the Special Issue Recent Advances in Harmonic Analysis and Applications)
21 pages, 342 KiB  
Article
Variation Inequalities for the Hardy-Littlewood Maximal Function on Finite Directed Graphs
by Feng Liu and Xiao Zhang
Mathematics 2022, 10(6), 950; https://doi.org/10.3390/math10060950 - 16 Mar 2022
Viewed by 1731
Abstract
In this paper, the authors establish the bounds for the Hardy-Littlewood maximal operator defined on a finite directed graph G→ in the space BVp(G→) of bounded p-variation functions. More precisely, the authors obtain the BVp [...] Read more.
In this paper, the authors establish the bounds for the Hardy-Littlewood maximal operator defined on a finite directed graph G→ in the space BVp(G→) of bounded p-variation functions. More precisely, the authors obtain the BVp norms of MG→ for some directed graphs G→. Full article
(This article belongs to the Special Issue Recent Advances in Harmonic Analysis and Applications)
12 pages, 295 KiB  
Article
A Note on the Boundedness of Doob Maximal Operators on a Filtered Measure Space
by Wei Chen and Jingya Cui
Mathematics 2021, 9(22), 2953; https://doi.org/10.3390/math9222953 - 18 Nov 2021
Viewed by 1624
Abstract
Let M be the Doob maximal operator on a filtered measure space and let v be an Ap weight with 1<p<+∞. We try proving that [...] Read more.
Let M be the Doob maximal operator on a filtered measure space and let v be an Ap weight with 1<p<+∞. We try proving that ∥Mf∥Lp(v)≤p′[v]Ap1p−1∥f∥Lp(v), where 1/p+1/p′=1. Although we do not find an approach which gives the constant p′, we obtain that ∥Mf∥Lp(v)≤p1p−1p′[v]Ap1p−1∥f∥Lp(v), with limp→+∞p1p−1=1. Full article
(This article belongs to the Special Issue Recent Advances in Harmonic Analysis and Applications)
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Review

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8 pages, 272 KiB  
Review
A Survey on the Study of Generalized Schrödinger Operators along Curves
by Wenjuan Li, Huiju Wang and Qingying Xue
Mathematics 2023, 11(1), 8; https://doi.org/10.3390/math11010008 - 20 Dec 2022
Viewed by 1318
Abstract
In this survey, we review the historical development for the Carleson problem about the a.e. pointwise convergence in five aspects: the a.e. convergence for generalized Schrödinger operators along vertical lines; a.e. convergence for Schrödinger operators along arbitrary single curves; a.e. convergence for Schrödinger [...] Read more.
In this survey, we review the historical development for the Carleson problem about the a.e. pointwise convergence in five aspects: the a.e. convergence for generalized Schrödinger operators along vertical lines; a.e. convergence for Schrödinger operators along arbitrary single curves; a.e. convergence for Schrödinger operators along a family of restricted curves; upper bounds of p for the Lp-Schrödinger maximal estimates; and a.e. convergence rate for generalized Schrödinger operators along curves. Finally, we list some open problems which need to be addressed. Full article
(This article belongs to the Special Issue Recent Advances in Harmonic Analysis and Applications)
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