- Relations between Kondratiev areas and refined localization Triebel-Lizorkin areas
Authors: Markus Hansen, Benjamin Scharf, Cornelia Schneider
Summary: We examine the shut relation between sure weighted Sobolev areas (Kondratiev areas) and refined localization areas from launched by Triebel [39,40]. Specifically, utilizing a characterization for refined localization areas from Scharf [32], we significantly enhance an embedding from Hansen [17]. This embedding is of particular curiosity in reference to convergence charges for adaptive approximation schemes.
2. A linear operator bounded in all Besov however not in Triebel-Lizorkin areas
Authors: Liding Yao
Summary: 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, however T(Fspq(Rn))⊄Fspq(Rn) until p=q. Consequently Triebel-Lizorkin areas can’t be interpolated from Besov areas until p=q. Within the appendix we objective a query for the interpolation framework through structured Banach areas.
