Optimal embeddings of critical Sobolev-Lorentz-Zygmund spaces

Hidemitsu Wadade. "Optimal embeddings of critical Sobolev-Lorentz-Zygmund spaces." Studia Mathematica 223.1 (2014): 77-95. <http://eudml.org/doc/285381>.

@article{HidemitsuWadade2014,
abstract = {We establish the embedding of the critical Sobolev-Lorentz-Zygmund space $H^\{n/p\}_\{p,q,λ₁,...,λₘ\}(ℝⁿ)$ into the generalized Morrey space $ℳ_\{Φ,r\}(ℝⁿ)$ with an optimal Young function Φ. As an application, we obtain the almost Lipschitz continuity for functions in $H^\{n/p + 1\}_\{p,q,λ₁,...,λₘ\}(ℝⁿ)$. O’Neil’s inequality and its reverse play an essential role in the proofs of the main theorems.},
author = {Hidemitsu Wadade},
journal = {Studia Mathematica},
keywords = {Sobolev-Lorentz-Zygmund space; generalized Morrey space; almost Lipschitz continuity},
language = {eng},
number = {1},
pages = {77-95},
title = {Optimal embeddings of critical Sobolev-Lorentz-Zygmund spaces},
url = {http://eudml.org/doc/285381},
volume = {223},
year = {2014},
}

TY - JOUR
AU - Hidemitsu Wadade
TI - Optimal embeddings of critical Sobolev-Lorentz-Zygmund spaces
JO - Studia Mathematica
PY - 2014
VL - 223
IS - 1
SP - 77
EP - 95
AB - We establish the embedding of the critical Sobolev-Lorentz-Zygmund space $H^{n/p}_{p,q,λ₁,...,λₘ}(ℝⁿ)$ into the generalized Morrey space $ℳ_{Φ,r}(ℝⁿ)$ with an optimal Young function Φ. As an application, we obtain the almost Lipschitz continuity for functions in $H^{n/p + 1}_{p,q,λ₁,...,λₘ}(ℝⁿ)$. O’Neil’s inequality and its reverse play an essential role in the proofs of the main theorems.
LA - eng
KW - Sobolev-Lorentz-Zygmund space; generalized Morrey space; almost Lipschitz continuity
UR - http://eudml.org/doc/285381
ER -