Let $0 <p < q < \infty$. Why exactly does the inclusion $L_{\mathrm{loc}}^q(\mathbb{R}^n) \subseteq L_{\mathrm{loc}}^p(\mathbb{R}^n)$ hold?
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Holder's inequality. – Aug 21 '16 at 21:16
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3This might be similar http://math.stackexchange.com/questions/66029/lp-and-lq-space-inclusion – iamvegan Aug 21 '16 at 21:21
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Thanks a lot. I totally forgot the regularity of the Lebesgue measure. – TheGeekGreek Aug 28 '16 at 09:31