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/lp/de-gruyter/trace-operators-on-fractals-entropy-and-approximation-numbers-0MalD76P0D
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- Publisher
- de Gruyter
- Copyright
- © de Gruyter 2011
- ISSN
- 1072-947X
- eISSN
- 1072-9176
- DOI
- 10.1515/GMJ.2011.0030
- Publisher site
- See Article on Publisher Site
Abstract
First we compute the trace space of Besov spaces – characterized via atomic decompositions – on fractals ΓΓ, for parameters 0 < p < ∞, 0 < q ≤≤ min(1, p ) and s = ( n – d )/ p . New Besov spaces on fractals are defined via traces for 0 < p, q ≤≤ ∞, s ≥ ( n – d )/ p and some embedding assertions are established. We conclude by studying the compactness of the trace operator Tr ΓΓ by giving sharp estimates for entropy and approximation numbers of compact embeddings between Besov spaces. Our results on Besov spaces remain valid considering the classical spaces defined via differences. The trace results are used to study traces in Triebel–Lizorkin spaces as well.
Journal
Georgian Mathematical Journal – de Gruyter
Published: Sep 1, 2011
Keywords: Besov spaces; Triebel–Lizorkin spaces; d -sets; traces; entropy numbers; approximation numbers