Sharp embedding results for spaces of smooth functions with power weights

Martin Meyries, and Mark Veraar. "Sharp embedding results for spaces of smooth functions with power weights." Studia Mathematica 208.3 (2012): 257-293. <http://eudml.org/doc/285667>.

@article{MartinMeyries2012,
abstract = {We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on $ℝ^\{d\}$, equipped with power weights $w(x) = |x|^\{γ\}$, γ > -d. We prove two-weight Sobolev embeddings for these spaces. Moreover, we precisely characterize for which parameters the embeddings hold. The proofs are presented in such a way that they also hold for vector-valued functions.},
author = {Martin Meyries, Mark Veraar},
journal = {Studia Mathematica},
keywords = {weighted function spaces; vector-valued function spaces; Besov spaces; Triebel-Lizorkin spaces; Bessel-potential spaces; Sobolev spaces; Sobolev embedding; Nikol’skiĭ inequality; Jawerth-Franke embeddings},
language = {eng},
number = {3},
pages = {257-293},
title = {Sharp embedding results for spaces of smooth functions with power weights},
url = {http://eudml.org/doc/285667},
volume = {208},
year = {2012},
}

TY - JOUR
AU - Martin Meyries
AU - Mark Veraar
TI - Sharp embedding results for spaces of smooth functions with power weights
JO - Studia Mathematica
PY - 2012
VL - 208
IS - 3
SP - 257
EP - 293
AB - We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on $ℝ^{d}$, equipped with power weights $w(x) = |x|^{γ}$, γ > -d. We prove two-weight Sobolev embeddings for these spaces. Moreover, we precisely characterize for which parameters the embeddings hold. The proofs are presented in such a way that they also hold for vector-valued functions.
LA - eng
KW - weighted function spaces; vector-valued function spaces; Besov spaces; Triebel-Lizorkin spaces; Bessel-potential spaces; Sobolev spaces; Sobolev embedding; Nikol’skiĭ inequality; Jawerth-Franke embeddings
UR - http://eudml.org/doc/285667
ER -