  We study Volterra processes $X_t = \int_0^t K(t,s) dW_s$, where $W$ is a
standard Wiener process, and the kernel has the form $K(t,s) = a(s) \int_s^t
b(u) c(u-s) du$. This form generalizes the Volterra kernel for fractional
Brownian motion (fBm) with Hurst index $H>1/2$. We establish smoothness
properties of $X$, including continuity and Holder property. It happens that
its Holder smoothness is close to well-known Holder smoothness of fBm but is a
bit worse. We give a comparison with fBm for any smoothness theorem. Then we
investigate the problem of inverse representation of $W$ via $X$ in the case
where $c\in L^1[0,T]$ creates a Sonine pair, i.e. there exists $h\in L^1[0,T]$
such that $c * h = 1$. It is a natural extension of the respective property of
fBm that generates the same filtration with the underlying Wiener process.
Since the inverse representation of the Gaussian processes under consideration
are based on the properties of Sonine pairs, we provide several examples of
Sonine pairs, both well-known and new.
  Key words: Gaussian process, Volterra process, Sonine pair, continuity,
Holder property, inverse representation.
