Embedding of $L_p$ spaces of Metrizable Measurable Group.

11 Views Asked by At

Let $G$ be a $\sigma$-locally compact and metrizable topological group equipped with the left Haar measure $\mu$. When can $L^p_{\mu}(G)$ be Bi-Lipschitzly embedded into a Lebesgue space on a Euclidean space (wrt the Lebesgue measure)?