- Relations between Kondratiev areas and refined localization Triebel-Lizorkin areas
Authors: Markus Hansen, Benjamin Scharf, Cornelia Schneider
Abstract: We study the shut relation between certain weighted Sobolev areas (Kondratiev areas) and refined localization areas from launched by Triebel [39,40]. Particularly, using a characterization for refined localization areas from Scharf [32], we considerably improve an embedding from Hansen [17]. This embedding is of explicit curiosity in reference to convergence prices for adaptive approximation schemes.
2. A linear operator bounded in all Besov nevertheless not in Triebel-Lizorkin areas
Authors: Liding Yao
Abstract: We assemble a linear operator T:S′(Rn)→S′(Rn) such that T:Bspq(Rn)→Bspq(Rn) for all 0<p,q≤∞ and s∈R, nevertheless T(Fspq(Rn))⊄Fspq(Rn) till p=q. Consequently Triebel-Lizorkin areas cannot be interpolated from Besov areas till p=q. Inside the appendix we goal a question for the interpolation framework by way of structured Banach areas.
