Full paper in PDF:
$%H. Triebel, Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers, Rev. Mat. Complut. 15 (2002), no. 2, 475–524.%$

Function spaces of type and cover as special cases classical and fractional Sobolev spaces, classical Besov spaces, Hölder-Zygmund spaces and inhomogeneous Hardy spaces. In the last 2 or 3 decades they haven been studied preferably on and in smooth bounded domains in including numerous applications to pseudodifferential operators, elliptic boundary value problems etc. To a lesser extent spaces of this type have been considered in Lipschitz domains. But in recent times there is a growing interest to study and to use spaces of this type in Lipschitz domains and on their boundaries. It is the aim of this paper to deal with function spaces of and type in Lipschitz domains and on Lipschitz manifolds in a systematic (although not comprehensive) way: We describe and comment on known results, seal some gaps, give new proofs, and add a few new results of relevant aspects.

2000 Mathematics Subject Classification: 46E35.