Comparison of Morrey spaces and Nikol'skii spaces

We consider two popular function spaces: the Morrey spaces and the Nikol'skii spaces and investigate the relationship between them in the one-dimensional case. In particular, we prove that, under the appropriate assumptions on the numerical parameters, their restrictions to the class of functions f of the form $f(x) = g(|x|)$, where g is a non-negative non-increasing function on $[0,\infty)$, coincide.