  We calculated the energy spectra and the fluxes of electron neutrinos in
extragalactic space emitted in the process of the evaporation of primordial
black holes (PBHs) in the early universe. It was assumed that PBHs are formed
by a blue power-law spectrum of primordial density fluctuations. In the
calculations of neutrino spectra the spectral index of density fluctuations and
the reheating temperature were used as free parameters. The absorption of
neutrinos during propagation in the space was taken into account. We obtained
the bounds on the spectral index assuming validity of the standard picture of
gravitational collapse and using the available data of several experiments with
atmospheric and solar neutrinos. The comparison of our results with the
previous constraints (which had been obtained using diffuse photon background
data) shows that such bounds are quite sensitive to an assumed form of the
initial PBH mass function.
