  Fractional-order strongly elliptic pseudodifferential operators $P$ with
homogeneous $x$-independent symbol satisfy a principal $\mu $-transmission
condition relative to $R^n_+$. It is shown that the solutions of the
homogeneous Dirichlet problem for $P$ on $R^n_+$ have a regularity property
with factor $x_n^\mu $ in low-order Sobolev spaces, and that integration by
parts formulas hold.
  The results apply in particular to nonsymmetric operators with real kernel,
that were treated unsatisfactorily in an earlier paper arXiv:2012.13964.
