I will prove some results in the direction of answering a question of Lovasz about the norms defined by certain combinatorial structures. Inspired by the similarity of the definitions of $L_p$ norms, trace norms, and Gowers norms, we introduce and study a wide class of norms containing these, as well as many other norms. It will be proven that every norm in this class must satisfy a Cauchy-Schwarz-Gowers type inequality. I will show an application of this inequality to a conjecture of Erdos-Simonovits and Sidorenko about subgraph densities.