  In this paper we investigate Besov spaces on graded Lie groups. We prove a
Nikolskii type inequality (or the Reverse H\"older inequality) on graded Lie
groups and as consequence we obtain embeddings of Besov spaces. We prove a
version of the Littlewood-Paley theorem on graded Lie groups. The results are
applied to obtain embedding properties of Besov spaces and multiplier theorems
for both spectral and Fourier multipliers in Besov spaces on graded Lie groups.
In particular, we give a number of sufficient conditions for the boundedness of
Fourier multipliers in Besov spaces.
