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In this note we extend a theorem of Kwong and Zettl concerning the inequality
The Kwong-Zettl result holds for 1 ≤ p < ∞ and real numbers α, β, γ such that the conditions (i) β = (α + γ)/2, (ii) β > - 1 , and (iii) γ - 1 - p hold. Here the inequality is proved with β satisfying (i) for all α, γ except p — 1,-1 — p. In this case the inequality is false; however u is shown to satisfy the inequality
