Recent Developments of Function Spaces and Their Applications II

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 December 2024 | Viewed by 1952

Special Issue Editors


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Guest Editor
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Interests: harmonic analysis; function space; boundedness of operators
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Interests: harmonic analysis; function space; boundedness of operators
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As one of the central topics of modern harmonic analysis, the theory of function spaces has found wide applications in various branches of mathematics, such as harmonic analysis, partial differential equations, geometric analysis, and potential analysis, and has, for a long time, received a lot of attention. The development of various function spaces on different underlying spaces provides many new working spaces for the research of other related analysis fields.

As a continuation of the issue “Recent Developments of Function Spaces and Their Applications I”, this Special Issue, entitled “Recent Developments of Function Spaces and Their Applications II”, is devoted to collecting recent progress on the theory of function spaces as well as on their applications in harmonic analysis, boundedness of operators, or partial differential equations. We would like to invite original research articles that provide new results on this subject. The topics of interest include, but are not limited to the keywords listed as follows.

Prof. Dr. Dachun Yang
Prof. Dr. Wen Yuan
Guest Editors

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Keywords

  • (weighted) Lebesgue space
  • Morrey space
  • Bourgain-Morrey space
  • Orlicz space
  • Lorentz space
  • Sobolev space
  • Hardy space
  • Herz space
  • BMO
  • John-Nirenberg space
  • Besov space
  • Triebel-Lizorkin space
  • Campanato space
  • (ball) quasi-Banach function space
  • Hilbert transform
  • Riesz transform
  • Calderón-Zygmund operator
  • multiplier
  • trace
  • interpolation
  • embedding
  • extension
  • dual
  • decomposition via atoms
  • molecules, or wavelets
  • frame
  • Muckenhoupt (matrix) weight
  • domain
  • space of homogeneous type
  • metric measure space

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Published Papers (2 papers)

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Research

10 pages, 272 KiB  
Article
Lp-Boundedness of a Class of Bi-Parameter Pseudo-Differential Operators
by Jinhua Cheng
Mathematics 2024, 12(11), 1653; https://doi.org/10.3390/math12111653 - 24 May 2024
Viewed by 799
Abstract
In this paper, I explore a specific class of bi-parameter pseudo-differential operators characterized by symbols σ(x1,x2,ξ1,ξ2) falling within the product-type Hörmander class Sρ,δm. This classification [...] Read more.
In this paper, I explore a specific class of bi-parameter pseudo-differential operators characterized by symbols σ(x1,x2,ξ1,ξ2) falling within the product-type Hörmander class Sρ,δm. This classification imposes constraints on the behavior of partial derivatives of σ with respect to both spatial and frequency variables. Specifically, I demonstrate that for each multi-index α,β, the inequality |ξαxβσ(x1,x2,ξ1,ξ2)|Cα,β(1+|ξ|)mi=12(1+|ξi|)ρ|αi|+δ|βi| is satisfied. My investigation culminates in a rigorous analysis of the Lp-boundedness of such pseudo-differential operators, thereby extending the seminal findings of C. Fefferman from 1973 concerning pseudo-differential operators within the Hörmander class. Full article
(This article belongs to the Special Issue Recent Developments of Function Spaces and Their Applications II)
12 pages, 248 KiB  
Article
3-Complex Symmetric and Complex Normal Weighted Composition Operators on the Weighted Bergman Spaces of the Half-Plane
by Zhi-Jie Jiang
Mathematics 2024, 12(7), 980; https://doi.org/10.3390/math12070980 - 25 Mar 2024
Viewed by 767
Abstract
One of the aims of this paper is to characterize 3-complex symmetric weighted composition operators induced by three types of symbols on the weighted Bergman space of the right half-plane with the conjugation [...] Read more.
One of the aims of this paper is to characterize 3-complex symmetric weighted composition operators induced by three types of symbols on the weighted Bergman space of the right half-plane with the conjugation Jf(z)=f(z¯)¯. It is well known that the complex symmetry is equivalent to 2-complex symmetry for the weighted composition operators studied in the paper. However, the interesting fact that 3-complex symmetry is not equivalent to 2-complex symmetry for such operators is found in the paper. Finally, the complex normal of such operators on the weighted Bergman space of the right half-plane with the conjugation J is characterized. Full article
(This article belongs to the Special Issue Recent Developments of Function Spaces and Their Applications II)
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