Monatshefte für Mathematik

, Volume 171, Issue 3, pp 443–457

On traces of general decomposition spaces


DOI: 10.1007/s00605-013-0532-z

Cite this article as:
Nielsen, M. Monatsh Math (2013) 171: 443. doi:10.1007/s00605-013-0532-z


The decomposition space approach is a general method to construct smoothness spaces on \(\mathbb{R }^d\) that include Besov, Triebel–Lizorkin, modulation, and \(\alpha \)-modulation spaces as special cases. This method also handles isotropic and an-isotropic spaces within the same framework. In this paper we consider a trace theorem for general decomposition type smoothness spaces. The result is based on a simple geometric estimate related to the structure of coverings of the frequency space used in the construction of decomposition spaces.


Trace operator Decomposition space \(\alpha \)-modulation space  Besov space Triebel–Lizorkin space 

Mathematics Subject Classification (2000)

42C15 46E35 47B25 

Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesAalborg UniversityAalborg EastDenmark

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