Embedding of Lipschitz classes into classes of functions of Λ-bounded variation

In this note, sufficient or necessary conditions for embedding of Lipschitz classes H p ω , 1 ⩽ p < ∞ into classes ΛBV of functions of Λ-bounded variation are considered. Based on the technique of decomposition of functions, we obtain sufficient and necessary conditions for the embedding H p α ⊂ { n β } BV , 0 < α , β ⩽ 1 .