Realizations of homogeneous Besov and Triebel–Lizorkin spaces and an application to pointwise multipliers

We study the dilation commuting realizations of the homogeneous Besov spaces [Formula: see text] or the homogeneous Triebel–Lizorkin spaces [Formula: see text] in the case p, q > 0, and either s - (n/p) ∉ ℕ0or s - (n/p) ∈ ℕ0and 0 < q ≤ 1 (0 < p ≤ 1 in the [Formula: see text]-case). We present an application to pointwise multiplication if s ≤ n/p.