Optimal embeddings of generalized Besov spaces

We prove optimal embeddings of generalized Besov spaces built-up over rearrangement invariant function spaces defined on $\mathbb R^n$ with the Lebesgue measure into other rearrangement invariant spaces in the subcritical or critical cases and into generalized Hölder–Zygmund spaces in the supercritical case. The investigation is based on some real interpolation techniques and estimates of the rearrangement of $f$ in terms of the modulus of continuity of $f$.