Операторы Хаусдорфа специального вида в пространствах типа BMO и пространствах Гёльдера-Липшица

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.