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We determine the trace of Besov spaces B s p,q (R n ) and Triebel-Lizorkin spaces F s p,q (R n )characterized via atomic decompositions -on hyperplanes R m , n > m ∈ N, for parameters 0 < p, q < ∞ and s > 1 p . The limiting case s = 1 p is investigated as well. We generalize these assertions to traces on the boundary Γ = ∂Ω of bounded C k domains Ω. 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,doi:10.4171/zaa/1409 fatcat:e5kloabklrfa3pghkvnfrl3jea