For a general measure space, we define : $\|f\|_p= \left(\int\vert f\vert^p du\right)^{1/p}$. Let $0 < a < b < c < \infty$ and prove the following: $$ \|f\|_b \leqslant \max\{\|f\|_a, \|f\|_c\}. $$ Any help is appreciated because I dont understand the solution underneath
Proof of an inequality of $L^p$ norms
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$\begingroup$
functional-analysis
inequality
norm
lp-spaces
. Hope this helps.
– 2012-11-19