Estimates of \(L_p\) modulus of continuity of generalized bounded variation classes (Q2249964)

Summary: Some sharp estimates of the \(L_p\) \((1\leq p<\infty)\) modulus of continuity of classes of \(\Lambda_{\varphi}\)-bounded variation are obtained. As direct applications, we obtain estimates of order of Fourier coefficients of functions of \(\Lambda_{\varphi}\)-bounded variation, and we also characterize some sufficient and necessary conditions for the embedding relations \(H_p^{\omega}\subset \Lambda_{\varphi}BV\). Our results include the corresponding known results of the class \(\Lambda BV\) as a special case.