Estimates of L p Modulus of Continuity of Generalized Bounded Variation Classes

Abstract EN

Some sharp estimates of the L p 1 ≤ p < ∞ modulus of continuity of classes of Λ φ -bounded variation are obtained.

As direct applications, we obtain estimates of order of Fourier coefficients of functions of Λ φ -bounded variation, and we also characterize some sufficient and necessary conditions for the embedding relations H p ω ⊂ Λ φ B V .

Our results include the corresponding known results of the class Λ B V as a special case.