The use of real-time applications in the packet networks is setting new requirements for the packet delivery. The current best-eort model in the Internet does not facilitate control over important characteristics such as delay, jitter and packet loss, which is needed for the proper operation of applications with real-time requirements. The main focus during the last years on providing QoS in IP...

We establish Stechkin-Marchaud-type inequalities for some Feller operators by using some modified Ditzian-Totik modulus of smooth -ness. Then we derive some inverse results for this family of operators. Moreover combining the inverse results with the direct estimates we obtain a approximation equivalent theorem.

For Lp spaces on Td, Rd and Sd−1 sharp versions of the classical Marchaud inequality are known. These results are extended here to Orlicz spaces (on Td, Rd and Sd−1) for which M(u1/q) is convex for some q, 1 < q ≤ 2, where M(u) is the Orlicz function. Sharp converse inequalities for such spaces are deduced.