Abstract
In the paper we study the fractional maximal commutators \(M_{b,\alpha }\) and the commutators of the fractional maximal operator \([b, M_{\alpha }]\) in the Orlicz spaces \(L^{\Phi }(\mathbb {G})\) on any stratified Lie group \(\mathbb {G}\). We give necessary and sufficient conditions for the boundedness of the operators \(M_{b,\alpha }\) and \([b, M_{\alpha }]\) on Orlicz spaces \(L^{\Phi }(\mathbb {G})\) when b belongs to \(BMO(\mathbb {G})\) spaces, whereby some new characterizations for certain subclasses of \(BMO(\mathbb {G})\) spaces are obtained.
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The author thanks the referee(s) for careful reading the paper and useful comments. The research of author was partially supported by grant of Cooperation Program 2532 TUBITAK—RFBR (RUSSIAN foundation for basic research) (Agreement Number No. 119N455), by Grant of 1st Azerbaijan-Russia Joint Grant Competition (Agreement Number No. EIF-BGM-4-RFTF-1/2017-21/01/1-M-08) and by the RUDN University Strategic Academic Leadership Program.
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Guliyev, V.S. Some Characterizations of BMO Spaces via Commutators in Orlicz Spaces on Stratified Lie Groups. Results Math 77, 42 (2022). https://doi.org/10.1007/s00025-021-01578-0
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DOI: https://doi.org/10.1007/s00025-021-01578-0