Faculty of Mathematics and Statistics
Ton Duc Thang University, Ho Chi Minh City, Vietnam
email: letrungnghia@tdtu.edu.vn, letrungnghia85@yahoo.com
Le Trung Nghia
Abstract:
In this article, we study the boundedness of operators of Hardy type on generalized
central function spaces, such as the generalized central Hardy space
\(\mathbf{HA}^{p,r}_\varphi(\mathbb{R}^n)\), the generalized central Morrey space
\(\dot{\mathbf{M}}^{p,r}_\varphi (\mathbb{R}^n)\), and the generalized central
Campanato space \(\dot{{\rm CMO}}^{p,r}_\varphi (\mathbb{R}^n)\), with \(p\in(1,\infty)\),
and \(\varphi(t):(0,\infty)\to (0,\infty)\).
We first show that \(\mathbf{HA}^{p',r'}_\varphi (\mathbb{R}^n)\) is the predual of
\(\dot{{\rm CMO}}^{p,r}_\varphi (\mathbb{R}^n)\). After that, we investigate the
boundedness of operators of Hardy type on those spaces.
By duality, we obtain the boundedness characterization of function
\(b\in \dot{{\rm CMO}}^{p,r}_\varphi (\mathbb{R}^n)\) via the
\(\dot{\textbf{M}}^{p,r}_\varphi (\mathbb{R}^n)\)-boundedness of commutator
\([b,\mathcal{H}^*]\).
Submitted July 2, 2025. Published August 8, 2025.
Math Subject Classifications: 42B20, 42B35, 42B30, 46A20.
Key Words: Hardy operators; commutator; generalized central function space; central atomic space.
DOI: 10.58997/ejde.2025.82
Show me the PDF file (431 KB), TEX file for this article.
|
Le Trung Nghia Faculty of Mathematics and Statistics Ton Duc Thang University, Ho Chi Minh City, Vietnam email: letrungnghia@tdtu.edu.vn, letrungnghia85@yahoo.com |
|---|
Return to the EJDE web page