We consider kernel regression estimate when both the response variable and the explanatory one are functional. The rates of uniform almost complete convergence are stated as function of the small ball probability of the predictor and as function of the entropy of the set on which uniformity is obtained.
"Kernel regression with functional response." Electron. J. Statist. 5 159 - 171, 2011. https://doi.org/10.1214/11-EJS600