The Trudinger inequality is true for $M^{1,s}$ spaces

Ryan Alvarado, Ahmed Dughayshim, Piotr Hajłasz

We prove the Trudinger inequality with exponent $\frac{s}{s-1}$ for $M^{1,s}$ Sobolev spaces on metric measure spaces under the sole measure growth assumption $\mu (B(x,r))\ge b{r}^s$.…