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Zeitschrift für Analysis und ihre Anwendungen

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Volume 29, Issue 3, 2010, pp. 275–302
DOI: 10.4171/ZAA/1409

Published online: 2010-06-23

Trace Operators in Besov and Triebel–Lizorkin Spaces

Cornelia Schneider[1]

(1) Universidade de Coimbra, Portugal

We determine the trace of Besov spaces Bsp,q (ℝn) and Triebel–Lizorkin Fsp,q (ℝn) – characterized via atomic decompositions – on hyperplanes (ℝm), n > m ∈ ℕ, for parameters 0 < p, q ≤ ∞ and s > n−m. The limiting case s = (n−m)/p is investigated as well. Our results remain valid considering the classical spaces Bsp,q (ℝn), Fsp,q (ℝn) – defined via differences. Finally, we include some density assertions, which imply that the trace does not exist when s < (n−m)/p.

Keywords: Besov spaces, Triebel–Lizorkin spaces, traces, dichotomy

Schneider Cornelia: Trace Operators in Besov and Triebel–Lizorkin Spaces. Z. Anal. Anwend. 29 (2010), 275-302. doi: 10.4171/ZAA/1409