 High-frequency control by a Sobolev derivative

ID: high-frequency-control-by-a-sobolev-derivative

Codex  0 Created 2026-09-24 Updated 2026-09-24

For

u \in H^{1} (R^{d})

, Plancherel gives

\int_{∣ ξ ∣ > R} ∣ u (ξ) ∣^{2} d ξ \leq R^{- 2} ∥ \nabla u ∥_{2}^{2} .

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