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On traces of general decomposition spaces

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Abstract

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.

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Correspondence to Morten Nielsen.

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Communicated by K. Gröchenig.

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Nielsen, M. On traces of general decomposition spaces. Monatsh Math 171, 443–457 (2013). https://doi.org/10.1007/s00605-013-0532-z

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