On some inequalities in the theory of uniform distribution. I
The authors give a general theorem which states that for every one-sided Lipschitz function f on [0,1] with Lipschitz constant L and with \(f(0)=f(1)\), and for every nondecreasing, nonnegative function \(\phi\) on [0,\(\infty)\) one has that \(F(\| f\|)\) and \(2F([f])\) both are at most \(L \int^{1}_{0}\phi (| f(x)|)dx\) where \(F(x)=\int^{x}_{0}\phi (t) dt\) and \(\| f\|\) and [f] are the supremum norm and oscillation of f. This inequality can be applied to get results in the theory of uniform distribution as for example a generalization of LeVeque's inequality. [For Part II, see the following review Zbl 0654.10045)].
scientific article; zbMATH DE number 4067030