Nikol’skii inequalities for Lorentz–Zygmund spaces

Abstract

Analogs of the Nikol’skii inequality in Lorentz–Zygmund spaces are obtained for functions of the form $$\sum _{k=1}^{n}c_{k}\varphi _{k}$$ , where $$\left\{ \varphi _{k}\right\} $$ is a finite orthonormal system in $$L_2$$ bounded in $$L_\infty $$ . No assumptions about smoothness of considered functions are required. Used technique relies only on the properties of Lorentz–Zygmund spaces and Fourier series map. In addition, real interpolation method is applied.