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Mathematics > Functional Analysis

arXiv:2210.01468 (math)
[Submitted on 4 Oct 2022]

Title:Boundedness of some operators on grand generalized weighted Morrey spaces on RD-spaces

Authors:Suixin He, Shuangping Tao
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Abstract:The aim of this paper is to obtain the boundedness of some operator on grand generalized weighted Morrey spaces $\mathcal{L}^{p),\phi}_{\varphi}(\omega)$ over RD-spaces. Under assumption that functions $\varphi$ and $\phi$ satisfy certain conditions, the authors prove that Hardy-Littlewood maximal operator and $\theta$-type Calderón-Zygmund operator are bounded on grand generalized weighted Morrey spaces $\mathcal{L}^{p),\phi}_{\varphi}(\omega)$. Moreover, the boundedness of commutator $[b,T_{\theta}]$ which is generated by $\theta$-type Calderón-Zygmund operator $T_{\theta}$ and $b\in\mathrm{BMO}(\mu)$ on spaces $\mathcal{L}^{p),\phi}_{\varphi}(\omega)$ is also established. The results regarding the grand generalized weighted Morrey spaces is new even for domains of Euclidean spaces.
Comments: 15 pages
Subjects: Functional Analysis (math.FA)
MSC classes: 42B20(Primary), 42B35(Secondary)
Cite as: arXiv:2210.01468 [math.FA]
  (or arXiv:2210.01468v1 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.2210.01468

Submission history

From: Suixin He [view email]
[v1] Tue, 4 Oct 2022 08:44:00 UTC (9 KB)
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