Trace operators in Besov and Triebel-Lizorkin spaces

Abstract

We determine the trace of Besov spaces Bsp,q(ℝn) and Triebel-Lizorkin spaces F sp,q(ℝn) - characterized via atomic decompositions - on hyperplanes ℝm, n > m ∈ ℕ, 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 Bsp,q Fsp,q - defined via differences. Finally, we include some density assertions, which imply that the trace does not exist when s