Embedding relations of Besov classes under MVBV

Abstract

In this paper, we strengthen some of Leindler’s results from [L. Leindler. Embedding relations
of Besov classes. Acta Sci. Math. (Szeged), 73(2007)133-149.] under MVBV condition.
First, we discuss embedding relations between two Besov classes. Next, we give an equivalent estimate
for the k-order modulus of continuity of f (x) in Lp norm under MVBV condition. Finally,
we give the condition to ensure a function f 2 Lp having Fourier coecients of MVBV belongs
to the Besov class.