Trace operators in Besov and Triebel-Lizorkin spaces

摘要

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