Young’s inequality

Let ϕ: be a continuousMathworldPlanetmathPlanetmath , strictly increasing function such that ϕ(0)=0 . Then the following inequalityMathworldPlanetmath holds:


Equality only holds when b=ϕ(a). This inequality can be demonstrated by drawing the graph of ϕ(x) and by observing that the sum of the two areas represented by the integralsDlmfPlanetmath above is greater than the area of a rectangle of sides a and b, as is illustrated in attachment.

Title Young’s inequality
Canonical name YoungsInequality
Date of creation 2013-03-22 13:19:25
Last modified on 2013-03-22 13:19:25
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 8
Author rspuzio (6075)
Entry type Theorem
Classification msc 26D15
Related topic YoungInequality