  The paper deals with partitions of hypergraphs into induced subhypergraphs
satisfying constraints on their degeneracy. Our hypergraphs may have multiple
edges, but no loops. Given a hypergraph $H$ and a sequence $f=(f_1,f_2, \ldots,
f_p)$ of $p\geq 1$ vertex functions $f_i:V(H) \to \mathbb{N}_0$ such that
$f_1(v)+f_2(v)+ \cdots + f_p(v)\geq d_H(v)$ for all $v\in V(H)$, we want to
find a sequence $(H_1,H_2, \ldots, H_p)$ of vertex disjoint induced
subhypergraphs containing all vertices of $H$ such that each hypergraph $H_i$
is strictly $f_i$-degenerate, that is, for every non-empty subhypergraph
$H'\subseteq H_i$ there is a vertex $v\in V(H')$ such that $d_{H'}(v)<f_i(v)$.
Our main result in this paper says that such a sequence of hypergraphs exists
if and only if $(H,f)$ is not a so-called hard pair. Hard pairs form a
recursively defined family of configurations, obtained from three basic types
of configurations by the operation of merging a vertex. Our main result has
several interesting applications related to generalized hypergraph coloring
problems.
