March 3, 2026

Pathological complex interpolation involving the space W l,∞

Key Points

The result shows that Hσ,ρ does not embed into the complex interpolation space for any θ between 0 and 1.
Specifically, the finding demonstrates a failure of boundedness when s is greater than 1/p, confirming problematic interpolation behavior.
Assessment reveals that the condition for interpolation can be weakened from s > 1/p to s > 0 without losing the failure of embedding.
This suggests a broader issue within functional analysis regarding complex interpolation and Sobolev spaces at large.

Abstract

In 2024 it was shown that a pathological situation occurs in the complexinterpolation between W^l (with l 0 integer) and otherSobolev spaces. Specifically, if d 2 is an integer, p (1, ) and s>1/p, then equationH^, (R^d) (H^s, p (R^d), W^l, (R^d) ), equationfor any (0, 1), where: = (1-) s+ l and: =p/ (1-). In this paper we extend this result showing that () still holds underthe weaker condition s>0.

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Cite this study

Eduard Curcă (Tue,) studied this question.

www.synapsesocial.com/papers/69a760eac6e9836116a2e2ec

Authors

Eduard Curcă

Actions

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Pathological complex interpolation involving the space W l,∞

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Cite this study

Authors

Actions

References and Citations

Citation Network

Connected Papers

Discussion