  We continue our study and applications of generalized H\"ormander spaces of
distributions $\mathcal{D}'_{\gamma,\Lambda}$ with $C^\infty$ wavefront set
included in a cone $\Lambda$ and the union of $H^s$-wave front sets in a second
cone $\gamma\subset \Lambda$. We give hypocontinuity results and failure of
continuity of tensor multiplication maps between these spaces and deduce
hypocontinuity results for various compositions on spaces of multilinear maps.
We apply this study to a generalization of microcausal functionals from
algebraic quantum field theory with derivatives controlled by spaces either of
the form $\mathcal{D}'_{\gamma,\Lambda}$ or some $\epsilon$-tensor product of
them. We prove nuclearity and completeness results and give general results to
build Poisson algebra structures (with at least hypocontinuous bilinear
products). We also apply our general framework to build retarded products with
field dependent propagators.
