On a Limiting Case for Pointwise Multiplication in Nikol'skii–Besov Spaces

We investigate the regularity of the set of all products $f\cdot g$ for $f$ and $g$ belonging to certain Nikol'skii–Besov spaces. The special situation we are interested in has been left open in earlier contributions. It represents a limiting situation. We list a number of positive and negative results, both in the inhomogeneous and in the homogeneous situation.