Pathological Complex Interpolation Involving the Space Wl,∞

ABSTRACT

In 2024 it was shown that a pathological situation occurs in the complex interpolation between (with integer) and other Sobolev spaces. Specifically, if is an integer, , and , then for any , where and .

In this paper we extend this result by showing that () still holds under the weaker condition . While the case can be handled by using traces on hyperplanes, the case requires trace theory on fractal sets.