A problem

The following problem was told to me by A. Meir. Let $$F\left( p \right): = \sqrt p \int_0^\infty {{{\left| {\frac{{\sin t}}{t}} \right|}^p}} dt.$$ Then \(F\left( 1 \right) = + \infty ,F\left( 2 \right) = \pi /\sqrt 2 .\)