Estimates of Lp modulus of continuity of generalized bounded variation classes

Some sharp estimates of the lp 1 ≤ p < ∞ 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 h p ω ⊂ λ b v. our results include the corresponding known results of the class λ b v as a special case. © 2014 heping wang and zhaoyang wu.