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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, Number 12, Pages 8–21
DOI: https://doi.org/10.26907/0021-3446-2020-12-8-21 (Mi ivm9631) 		 
Hausdorff operators of special kind in $BMO$-type spaces and Hölder–Lipschitz spaces

S. S. Volosivets

Saratov State University, 83 Astrakhanskaya str., Saratov, 410012 Russia
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DOI: https://doi.org/10.26907/0021-3446-2020-12-8-21
Abstract: We show that some $BMO$-type spaces are invariant with respect to the Hausdorff operators of special kind (weighted Hardy-Cesaro operators). Also we obtain a sufficient and necessary conditions for such operators to be bounded in spaces of functions of generalized bounded variation. Finally, we study the invariance of Hölder–Lipschitz spaces with respect to these operators.
Keywords: Hausdorff operator, Hölder–Lipschitz spaces, $VMO(\mathbb R^n)$, $bmo(\mathbb R^n)$, functions of generalized bounded variation.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FSRR-2020-0006
Received: 21.12.2019
Revised: 25.02.2020
Accepted: 29.06.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, Volume 64, Issue 12, Pages 6–19
DOI: https://doi.org/10.3103/S1066369X20120026
Bibliographic databases:
Document Type: Article
UDC: 517.518: 517.983
Language: Russian
Citation: S. S. Volosivets, “Hausdorff operators of special kind in $BMO$-type spaces and Hölder–Lipschitz spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 12, 8–21; Russian Math. (Iz. VUZ), 64:12 (2020), 6–19
Citation in format AMSBIB
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\pages 8--21
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\issue 12
\pages 6--19
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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