My question may looks very simple:
I know that $(a+b)^{2}\leq 2(a^{2}+b^{2})$ for any $a,b\in \mathbb R$. Do we have an inequality like $$(a+b)^{2} \leq C\, a^{p}b^{p}$$ for some constant $C$ depends only on the powers $2,p>0$?
Edit: $0 .
My question may looks very simple:
I know that $(a+b)^{2}\leq 2(a^{2}+b^{2})$ for any $a,b\in \mathbb R$. Do we have an inequality like $$(a+b)^{2} \leq C\, a^{p}b^{p}$$ for some constant $C$ depends only on the powers $2,p>0$?
Edit: $0 .