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Hausdorff Operators of Special Kind in BMO-type Spaces and Hölder–Lipschitz Spaces

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Abstract

We show that some BMO-type spaces are invariant with respect to Hausdorff operators of a special kind (weighted Hardy–Cesáro operators). Moreover, we establish the necessary and sufficient conditions for the boundedness of such operators in spaces of functions of generalized bounded variation. We study the invariance of Hölder–Lipschitz spaces with respect to these operators.

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Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of the state assignment (project no. FSRR-2020-0006).

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Correspondence to S. S. Volosivets.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 8–21.

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Volosivets, S.S. Hausdorff Operators of Special Kind in BMO-type Spaces and Hölder–Lipschitz Spaces. Russ Math. 64, 6–19 (2020). https://doi.org/10.3103/S1066369X20120026

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  • DOI: https://doi.org/10.3103/S1066369X20120026

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