  We find exact small deviation asymptotics with respect to weighted Hilbert
norm for some well-known Gaussian processes. Our approach does not require the
knowledge of eigenfunctions of the covariance operator of a weighted process.
Such a peculiarity of the method makes it possible to generalize many previous
results in this area. We also obtain new relations connected to exact small
deviation asymptotics for a Brownian excursion, a Brownian meander, and Bessel
processes and bridges.
