Symplectic embeddings of the ${\mathrm{\ell }}_p$-sum of two discs

In this paper we study symplectic embedding questions for the ${\mathrm{\ell }}_p$-sum of two discs in ${\mathbb{R}}^4$, when $1\le p\le \mathrm{\infty }$. In particular, we compute the symplectic inner and outer radii in these cases, and show how different kinds of embedding rigidity and flexibility phenomena appear as a function of the parameter $p$.