Nikol’skii–Type Inequalities for Trigonometric Polynomials for Lorentz–Zygmund Spaces

Abstract

Nikol’skii–type inequalities, that is inequalities between different metrics of trigonometric polynomials on the torus Td for the Lorentz–Zygmund spaces, are obtained. The results of previous paper “Nikol’skii inequalities for Lorentz–Zygmund spaces” are extended. Applications to approximation spaces in Lorentz–Zygmund spaces and to Besov spaces are given.