On some Nikolskiǐ- and Oswald-type inequalities (Q1109257)

Inequalities are of great value in several contexts. Here the author has developed and discussed in 5 sections through 3 theorems certain properties of inequalities. Estimation of pseudo-norms is one of the main objectives. Inequalities of Nikolskij in \(L^ p_{2\pi}\), \(p\geq 1\), and of Oswald with \(0<p<1\) are extended to the case of Orlicz spaces \(L^{\phi}_{2\pi}\). Two of the theorems can be applied to estimate the averaged moduli of smoothness in \(L^{\phi}_{2\pi}\) by means of best one-sided approximations in terms of trigonometric polynomials.