Exact constants for pointwise adaptive estimation under the Riesz transform

We consider nonparametric estimation of a multivariate function and its partial derivatives at a fixed point when the Riesz transform of the function is observed in Gaussian white noise. We assume that the unknown function belongs to some Sobolev class and construct an estimation procedure which achieves the best asymptotic minimax risk when the smoothness of the function is unknown.Writing of this article was financed by Deutsche Forschungsgemeinschaft under project MA1026/6-2 and Rolf Nevanlinna Institute.Mathematics Subject Classification (2000): 62G05, 62G20