A New Proof Of The Asymptotic Limit Of The $Lp$ Norm Of The Sinc   Function
  We improve on the inequality $\displaystyle{\frac{1}{\pi}\int_{-\infty}^{\infty} (\frac{\sin^2 t}{t^2})^pdt\leq \frac{1}{\sqrt p}, {0.2 cm}p\geq 1,}$ showing that $\displaystyle{\frac{1}{\pi}\int_{-\infty}^{\infty} (\frac{\sin^2 t}{t^2})^pdt\leq C(p) \frac{\sqrt{3/\pi}}{\sqrt p},}$ with $\displaystyle{\lim_{p\longrightarrow \infty} C(p)=1,}$ and indeed that {align*} \displaystyle{\lim_{p\longrightarrow \infty}\frac{1}{\pi}\int_{-\infty}^{\infty} (\frac{\sin^2 t}{t^2})^pdt/ \frac{\sqrt{3/\pi}}{\sqrt p}=1.} {align*} 
R. Kerman, S. Spektor
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