On dissonance of self-conformal measures in ${\mathbb{R}}^d$

Let $\mu$ be a self-conformal measure on ${\mathbb{R}}^d$. In this note we establish conditions for $\mu$ under which $\dim (\mu \ast \nu )=\min \{d,\dim \mu +\dim \nu \}$ holds when $\nu$ is any Ahlfors-regular or self-conformal measure on ${\mathbb{R}}^d$. Our main result states the following sufficient condition: $\mu$ is totally non-linear and not supported on a smooth hypersurface. We also establish sufficient (likely non-sharp) algebraic conditions for self-conformal measures which are not totally non-linear. The proofs combine recent results on scaling sceneries of self-conformal measures with a Marstrand-type projection theorem for product sets due to López and Moreira.