If $- \infty < a < b < \infty$, $0 < p < q < \infty$ how to prove that $L_{\infty}(a,b) \subset L_q(a,b) \subset L_p(a,b)$? Does anyone have any idea or some hints?
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Related: https://math.stackexchange.com/q/2241488/290189 – GNUSupporter 8964民主女神 地下教會 Oct 07 '18 at 14:04
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Holder's inequality could be useful – Keen-ameteur Oct 07 '18 at 14:09