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Let $G$ be a $p$ adic Lie group. In this work, we develop a dimension theoryfor coadmissible $G$ equivariant $D$ modules on smooth rigid analytic spacesand prove the inequality of Bernstein for the case of rigid analytic flagvarieties. In this setting, we then introduce the notion of weakly holonomic$G$ equivariant $\mathcal{D}$ modules. Finally, we define the duality functoron the category of weakly holonomic modules and study some of its properties.

Weak holonomicity for equivariant $\mathcal{D}$ modules on rigid analytic flag varieties