 Interpolation between L2 and Linfinity by a pointwise bound

ID: interpolation-between-l2-and-linfinity-by-a-pointwise-bound

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

For

2 \leq p < \infty

∥ h ∥_{p}^{p} \leq ∥ h ∥_{\infty}^{p - 2} ∥ h ∥_{2}^{2} .

Thus every function in

L^{2} \cap L^{\infty}

belongs to every

L^{p}

between them.

 New to topics? Read the docs here!