On the generalized Hardy's inequality of McGhee, Pigno and Smith and the problem of interpolation between BMO and a Besov space.

Piecewise Polynomial Approximation Methods in the Theory of Nikol’Skiĭ–Besov Spaces

“…For example, in [83], the interpolation problem for the BM O space and the Nikol'skiȋ-Besov space B λ p is solved for the case where p > 1. Moreover, results of [73] imply the interpolation theorem for the space of continuous function and B λ p for the case where 0 < p < 1.…”

“…and explain our reasoning. Firstly, we take into account the result of [83]. Secondly, we use the embedding of B d 1 into B d 1 (F (x)).…”

“…To interpolate the spaces on the left-hand side, we use the Peetre-Svensson theorem from [83]. It implies that BM O, B λ 1…”