Let $u\in D'(\mathbb{R}^n)$ be a distribution and suppose that $u$ can be extended to linear functional on $H^s$. Does it follow that $u$ can be extended to a continuous linear functional on $H^s$?
2026-04-06 02:23:28.1775442208
Continuity of the extension of a distribution to $H^s$
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As martini said: the existence of linear extension in the algebraic sense does not tell you anything. Such an extension can be shown to exist by following the proof of Hahn-Banach theorem without the majorizing functional.