  The purpose of the paper is to find explicit formulas describing the joint
distributions of the first hitting time and place for half-spaces of
codimension one for a diffusion in $\R^{n+1}$, composed of one-dimensional
Bessel process and independent n-dimensional Brownian motion. The most
important argument is carried out for the two-dimensional situation. We show
that this amounts to computation of distributions of various integral
functionals with respect to a two-dimensional process with independent Bessel
components. As a result, we provide a formula for the Poisson kernel of a
half-space or of a strip for the operator $(I-\Delta)^{\alpha/2}$,
$0<\alpha<2$. In the case of a half-space, this result was recently found, by
different methods, in [6]. As an application of our method we also compute
various formulas for first hitting places for the isotropic stable L\'evy
process.
