Negative Results concerning Fourier Series on the Complete Product of S3

The aim of this paper is to continue the studies about convergence in L-norm of the Fourier series based on representative product systems on the complete product of finite groups. We restrict our attention to bounded groups with unbounded sequence Ψ. The most simple example of this groups is the complete product of S3. In this case we proved the existence of an 1 < p < 2 number for which exists an f ∈ L such that its n-th partial sum of Fourier series Sn do not converge to the function f in L-norm. In this paper we extend this ”negative” result for all 1 < p <∞ and p 6= 2 numbers.