# $\ell^p$-spaces for $p<1$

It is well known that whenever $p\in (0,1)$, the mapping $$d_p(x,y):=\|x-y\|_{\ell^p}:=\left(\sum_{n=1}^\infty |x_n-y_n|^p\right)^\frac{1}{p}$$ turns $$\ell^p:=\{(x_n)_{n\in \mathbb N}:\|x\|_{\ell^p}<\infty\}$$ into a complete metric space.

Are there interesting applications of these spaces? I'm aware of the somewhat related Hamming distance, but I am wondering whether something more substantially mathematical exists.