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

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We show that some BMO-type spaces are invariant with respect to Hausdorff operators of a special kind (weighted Hardy–Cesaro operators). Moreover, we establish the necessary and sufficient conditions for the… Click to show full abstract

We show that some BMO-type spaces are invariant with respect to Hausdorff operators of a special kind (weighted Hardy–Cesaro 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 Holder–Lipschitz spaces with respect to these operators.

Keywords: operators special; bmo type; type spaces; lipschitz spaces; hausdorff operators; special kind

Journal Title: Russian Mathematics
Year Published: 2020

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