Nikol'skii inequalities for Lorentz-Zygmund spaces

Analogs of the Nikol'skii inequality in Lorentz-Zygmund spaces are obtained for functions of the form ∑nk=1ckfk, where {fk} is a finite orthonormal system in L2 bounded in LIF. 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.