  For a class of potentials $\psi$ satisfying a condition depending on the roof
function of a suspension (semi)flow, we show an EKP inequality, which can be
interpreted as a H\"older continuity property in the weak${^*}$ norm of
measures, with respect to the pressure of those measures, where the H\"older
exponent depends on the $L^q$-space that $\psi$ belongs to. This also captures
a new type of phase transition for intermittent (semi)flows (and maps).
