Intrinsic characterizations of distribution spaces on domains
Volume 127 / 1998
Studia Mathematica 127 (1998), 277-298
DOI: 10.4064/sm-127-3-277-298
Abstract
We give characterizations of Besov and Triebel-Lizorkin spaces $B_{pq}^{s}(Ω)$ and $F_{pq}^s(Ω)$ in smooth domains $Ω ⊂ ℝ^n$ via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.
