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Let $p$ be a prime. This papers aims at investigating sheaf cohomology of abroader class of $p$-adic period domains, other then the Drinfeld's upper halfspace (cf. \cite{O2}). Concretely, we let $\mathbf{G}$ be a split connectedreductive group over $\mathbb{Q}_p$ and restrict our attention to the $p$-adicperiod domain $\mathscr{F}^{\mathrm{wa}}$ which parametrizes the weaklyadmissible filtrations on the trivial $\mathbf{G}$-isocrystal inside a completeflag variety $\mathscr{F}$. Then, we consider sheaf cohomology of$\mathscr{F}^{\mathrm{wa}}$ with coefficients in vector bundles which areinduced by restriction of a homogeneous line bundle on $\mathscr{F}$ associatedto a dominant weight of $\mathbf{G}$.

On the sheaf cohomology of some $p$-adic period domains with coefficients in certain line bundles