In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality relating Lp spaces: let S be a measure space, let 1 ≤ p, q ≤ ∞ with 1/p + 1/q = 1, let f be in Lp(S) and g be in Lq(S). Then fg is in L1(S) and
For p = q = 2, we get the Cauchy-Schwarz inequality.
Hölder's inequality is used to prove the triangle inequality in the space Lp and also to establish that Lp is dual to Lq.