The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (344 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
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