Sharp embeddings between quasi-Banach Besov spaces and shallow ReLU variation spaces

Let $\mathcal D$ be the normalized ridge dictionary generated by $\operatorname{ReLU}^k$ on a bounded Lipschitz domain $Ω\subset\mathbb R^d$. We establish sharp embeddings between isotropic Besov spaces and the associated variation space $\mathcal L_1(\mathcal D)$ in the quasi-Banach range $0<p\le 1