On a theorem of Stanojević

Abstract

A new direct proof of a theorem of Stanojević is given. Consequently it is proven that the Fomin class F p ( 1 > p ⩽ 2 ) {\mathcal {F}_p}(1 > p \leqslant 2) is a subclass of the class B V ∩ C \mathcal {B}\mathcal {V} \cap \mathcal {C} , where C \mathcal {C} is the Garrett-Stanojević class and B V \mathcal {B}\mathcal {V} is the class of null sequences of bounded variation. This also provides a new direct proof of Fomin’s theorem.