  Sidorenko's Conjecture asserts that every bipartite graph H has the Sidorenko
property, i.e., a quasirandom graph minimizes the density of H among all graphs
with the same edge density. We study a stronger property, which requires that a
quasirandom multipartite graph minimizes the density of H among all graphs with
the same edge densities between its parts; this property is called the step
Sidorenko property. We show that many bipartite graphs fail to have the step
Sidorenko property and use our results to show the existence of a bipartite
edge-transitive graph that is not weakly norming; this answers a question of
Hatami [Israel J. Math. 175 (2010), 125-150].
