  For a split reductive group $G$ over a finite extension $L$ of ${\mathbb
Q}_p$, and a parabolic subgroup $P \subset G$ we introduce a category
${\mathcal O}^P$ which is equipped with a forgetful functor to the parabolic
category ${\mathcal O}^{\mathfrak p}$ of Bernstein, Gelfand and Gelfand. There
is a canonical fully faithful embedding of a subcategory ${\mathcal
O}^{\mathfrak p}_{\rm alg}$ of ${\mathcal O}^{\mathfrak p}$ into ${\mathcal
O}^P$, which 'splits' the forgetful map. We then introduce functors from the
category ${\mathcal O}^P$ to the category of locally analytic representations,
thereby generalizing the authors' previous work where these functors had been
defined on the category ${\mathcal O}^{\mathfrak p}_{\rm alg}$. It is shown
that these functors are exact, and a criterion for the irreducibility of a
representation in the image of this functor is proved.
