Clarkson's inequalities

In mathematics, Clarkson's inequalities, named after James A. Clarkson, are results in the theory of Lp spaces.

They give bounds for the Lp-norms of the sum and difference of two measurable functions in Lp in terms of the Lp-norms of those functions individually.

Let (X, Σ, μ) be a measure space; let f, g : X → R be measurable functions in Lp.

Then, for 2 ≤ p < +∞, For 1 < p < 2, where i.e., q = p ⁄ (p − 1).