Let $n$ be a natural number. Is it possible to write $$(x+y)^n \leq C(x^n + y^n)$$ for some constant $C$??
It is obvious for $n=2$ (using Young's inequality) but not obvious to me for other $n$.
Let $x$ and $y$ be positive reals.
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Sign up to join this communityLet $n$ be a natural number. Is it possible to write $$(x+y)^n \leq C(x^n + y^n)$$ for some constant $C$??
It is obvious for $n=2$ (using Young's inequality) but not obvious to me for other $n$.
Let $x$ and $y$ be positive reals.
$$(x+y)^n\leq(2\operatorname{Max}(x,y))^n\leq2^n(x^n+y^n)$$