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Proposition: CauchySchwarz Inequality for Integral pnorms
Let $[a,b]$ be a closed real interval, and let $f,g:[a,b]\to\mathbb R$ be two Riemannintegrable functions. The for the integral pnorms the CauchySchwarz inequality holds:
$$\int_{a}^bf(x)g(x)dx\le \left(\int_{a}^b (f(x))^2dx\right)^{\frac 12}\left(\int_{a}^b (g(x))^2dx\right)^{\frac 12}.$$
Table of Contents
Proofs: 1
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References
Bibliography
 Heuser Harro: "Lehrbuch der Analysis, Teil 1", B.G. Teubner Stuttgart, 1994, 11th Edition