Saffari–Sze´kely

Saffari’s Inequality If f : [0, 1] → R is bounded and measurable with H = M

[∞] [0,1](f) > 0, h = −M[−∞][0,1] (f) > 0, and if p = 1 or p ≥ 2, then

||f ||p ≤M[p−2]2 (H,h).

Comment The result is false if 1 < p < 2.