 Hölder interpolation inequality

ID: holder-interpolation-inequality

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

On a ball of radius

R

, lower derivative norms of

u \in C^{l, α}

are bounded by an arbitrarily small multiple of the top Hölder seminorm plus a multiple of

∥ u ∥_{C^{0}}

. One endpoint form is

R^{l} ∥ D^{l} u ∥_{0} \leq ε R^{l + α} [D^{l} u]_{α} + C_{ε} ∥ u ∥_{0} .

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