Trace Operators in Besov and Triebel–Lizorkin Spaces

Abstract

We determine the trace of Besov spaces Bs__p,q (ℝ_n_) and Triebel–Lizorkin Fs__p,q (ℝ_n_) – characterized via atomic decompositions – on hyperplanes (ℝ_m_), 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 Bs__p,q (ℝ_n_), Fs__p,q (ℝ_n_) – defined via differences. Finally, we include some density assertions, which imply that the trace does not exist when s < (n−m)/p.