Minimax Detection of a Signal for Besov Bodies and Balls

We consider an asymptotical minimax problem of detection of a signal from functional sets corresponding to the Besov balls $B^\sigma_{p,q}(C)$ or Besov bodies $\Theta^s_{p,q}(C)$ with a remote $L_2$-ball, the signal being observed in the Gaussian white noise of intensity $\varepsilon>0$, $\sigma>0$, $s=\sigma-1/p+1/2>0$. For the case of Besov bodies, for $q\geq p$ or $\min(p,q)\geq 2$, asymptotically exact estimates of the minimax probability of the detection errors are obtained, while for other cases and Besov balls, asymptotically exact conditions of the minimax distinguishability are found.