Comparison of Morrey Spaces and Nikol’skii Spaces

Abstract

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,∞), coincide.