Hardy operators and commutators on generalized central function spaces
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 generalize...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2025-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/82/abstr.html |
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| Summary: | 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
$[b,\mathcal{H}^*]$. |
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| ISSN: | 1072-6691 |