  We investigate minimax results for the anisotropic functional deconvolution
model when observations are affected by the presence of long-memory. Under
specific conditions about the covariance matrices of the errors, we follow a
standard procedure to construct an adaptive wavelet-based estimator that
attains asymptotically near-optimal convergence rates. These rates depend on
the parameter associated with the weakest long-range dependence, and
deteriorate as the intensity of long-memory increases. This behavior suggests
that the estimator adjusts to the best case scenario and that the weakest LM
dominates.
