Pullback functors for reduced and unreduced $$L^{q,p}$$-cohomology

In this paper we study the reduced and unreduced $L^{q,p}$-cohomology groups of oriented manifolds of bounded geometry and their behavior under uniform maps. A uniform map is a uniformly continuous map such that the diameter of the preimage of a subset is bounded in terms of the diameter of the subset itself. In general, for each $p,q \in [0, +\infty)$ , the pullback map along a uniform map does not induce a morphism between the spaces of p-integrable forms or even in $L^{qp}$-cohomology. Then our goal is to introduce, for each p in $[0, +\infty)$ and for each uniform map f between manifolds of bounded geometry, an $L^p$-bounded operator , such that it does induce in a functorial way the appropriate morphism in reduced and unreduced $L^{qp}$-cohomology.