Estimates ofLpModulus of Continuity of Generalized Bounded Variation Classes

Abstract

Some sharp estimates of the(1 ≤ < ∞) modulus of continuity of classes of Λ -bounded variation are obtained. As direct applications, we obtain estimates of order of Fourier coefficients of functions of Λ -bounded variation, and we also characterize some sufficient and necessary conditions for the embedding relations ⊂ Λ . Our results include the corresponding known results of the class Λ as a special case.2 Journal of Function Spaces and nondecreasing function ( ) on [0, ∞) such that ( ) ≡ 1 , 0 ≤ ≤ 1 and ( ) = , = 1, 2, . . ., then we say that ( ) generates Λ. By the nondecreasing property of Λ, it is easily verified that if ( ) generates Λ, then Submit your manuscripts at