Consider a normal model with unknown mean bounded by a known constant. This paper deals with minimax estimation of the squared mean. We establish an expression for the asymptotic minimax risk. This result is applied in nonparametric estimation of quadratic functionals.

T 2 are the only closed Riemann surfaces admitting nonconstant conformal mappings from the complex plane. The same rigidity is present in higher dimensions; closed manifolds admitting conformal mappings from Rn are quotients of Sn and Tn, see e.g. [2, Prop. 1.4]. However, if distortion is allowed, simple examples show that the spaces Sk1 × Sk2 × · · · × Skl (k1 + · · ·+ kl = n) receive nonconst...

The duality between Hl and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained . Using the atomic decomposition approach ([C], [L]) the author studied the problem of characterizing the dual space of Hl of vector-valued functions . In [B2] the author showed, for the case SZ = {Iz1 = 1}, tha...