On the set of $ \alpha $, $ p $-bounded variation of order $ h $

Abstract

In this paper we first explicit a subset of the set $ (l_p,l_u) $ for $ 1\le p<\infty $ and $ 0 0 $ real, generalizing the well-known set of $ p $-bounded variation $ bv_p=l_p(\Delta) $, and characterize martix transformations mapping from $ bv_p^h(\alpha) $ to $ bv_u^k(\beta) $ for $ 1\le p\le\infty $ and $ 0