Embedding relations of Besov classes under MVBV

Wen-Tao Cheng, Kan Yu, Ding-Yuan Chen

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 ∈ Lp having Fourier coefficients of MVBV belongs to the Besov class.