Characterization of fractional maximal operator and its commutators on Orlicz spaces in the Dunkl setting
| Autor: | Yagub Y. Mammadov, Fatma Muslumova, Vagif S. Guliyev |
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| Rok vydání: | 2020 |
| Předmět: |
Mathematics::Functional Analysis
Functional analysis Applied Mathematics Mathematics::Classical Analysis and ODEs Commutator (electric) Characterization (mathematics) Operator theory law.invention Combinatorics law Bounded function Maximal operator Algebra over a field Reflection group Analysis Mathematics |
| Zdroj: | Journal of Pseudo-Differential Operators and Applications. 11:1699-1717 |
| ISSN: | 1662-999X 1662-9981 |
| DOI: | 10.1007/s11868-020-00364-w |
| Popis: | On the $${\mathbb {R}}^{d}$$ the Dunkl operators $$\big \{D_{k,j}\big \}_{j=1}^{d}$$ are the differential-difference operators associated with the reflection group $${\mathbb {Z}}_2^d$$ on $${\mathbb {R}}^{d}$$ . In this paper, in the setting $${\mathbb {R}}^{d}$$ we find necessary and sufficient conditions for the boundedness of the fractional maximal operator $$M_{\alpha ,k}$$ on Orlicz spaces $$L_{\varPhi ,k}({\mathbb {R}}^{d})$$ . As an application of this result we show that $$b \in {\textit{BMO}}_{k}({\mathbb {R}}^{d})$$ if and only if the maximal commutator $$M_{b,k}$$ is bounded on Orlicz spaces $$L_{\varPhi ,k}({\mathbb {R}}^{d})$$ . |
| Databáze: | OpenAIRE |
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