When is the Haar measure a Pietsch measure for nonlinear mappings?
  We show that, as in the linear case, the normalized Haar measure on a compact topological group $G$ is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of $C(G)$. This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed. 
G. Botelho, D. Pellegrino, P. Rueda, J. Santos and J. B.   Seoane-Sep\'ulveda
math.FA