A subelliptic Bourgain–Brezis inequality

Wang, Yi, and Yung, Po-Lam. "A subelliptic Bourgain–Brezis inequality." Journal of the European Mathematical Society 016.4 (2014): 649-693. <http://eudml.org/doc/277172>.

@article{Wang2014,
abstract = {We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space $\dot\{NL\}^\{1,Q\}$ by $L^\{\infty \}$ functions, generalizing a result of Bourgain–Brezis. We then use this to obtain a Gagliardo–Nirenberg inequality for $$ on the Heisenberg group $\mathbb \{H\}^n$.},
author = {Wang, Yi, Yung, Po-Lam},
journal = {Journal of the European Mathematical Society},
keywords = {compensation phenomena; critical Sobolev embedding; homogeneous groups; Gagliardo-Nirenberg inequality; compensation phenomena; critical Sobolev embedding; homogeneous groups; Gagliardo-Nirenberg inequality},
language = {eng},
number = {4},
pages = {649-693},
publisher = {European Mathematical Society Publishing House},
title = {A subelliptic Bourgain–Brezis inequality},
url = {http://eudml.org/doc/277172},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Wang, Yi
AU - Yung, Po-Lam
TI - A subelliptic Bourgain–Brezis inequality
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 4
SP - 649
EP - 693
AB - We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space $\dot{NL}^{1,Q}$ by $L^{\infty }$ functions, generalizing a result of Bourgain–Brezis. We then use this to obtain a Gagliardo–Nirenberg inequality for $$ on the Heisenberg group $\mathbb {H}^n$.
LA - eng
KW - compensation phenomena; critical Sobolev embedding; homogeneous groups; Gagliardo-Nirenberg inequality; compensation phenomena; critical Sobolev embedding; homogeneous groups; Gagliardo-Nirenberg inequality
UR - http://eudml.org/doc/277172
ER -