1Abdus Salam School of Mathematical Sciences GC University Lahore 54600 Lahore, Pakistan 2Abdus Salam School of Mathematical Sciences GC University Lahore and Institute of Mathematics and Informatics Bulgarian Academy of Sciences 1113 Sofia, Bulgaria
Colloquium Mathematicum, Tome 123 (2011) no. 1, pp. 1-20
We prove optimal embeddings of homogeneous Sobolev spaces built over function spaces in ${\mathbb R}^n$
with $K$-monotone and rearrangement invariant norm into other rearrangement invariant function spaces.
The investigation is based on pointwise and integral estimates of the rearrangement or the oscillation of the rearrangement of $f$ in terms of the rearrangement of the derivatives of $f$.
Keywords:
prove optimal embeddings homogeneous sobolev spaces built function spaces mathbb k monotone rearrangement invariant norm other rearrangement invariant function spaces investigation based pointwise integral estimates rearrangement oscillation rearrangement terms rearrangement derivatives
Affiliations des auteurs :
Irshaad Ahmed
1
;
Georgi Eremiev Karadzhov
2
1
Abdus Salam School of Mathematical Sciences GC University Lahore 54600 Lahore, Pakistan
2
Abdus Salam School of Mathematical Sciences GC University Lahore and Institute of Mathematics and Informatics Bulgarian Academy of Sciences 1113 Sofia, Bulgaria
@article{10_4064_cm123_1_1,
author = {Irshaad Ahmed and Georgi Eremiev Karadzhov},
title = {Optimal embeddings of generalized homogeneous {Sobolev} spaces},
journal = {Colloquium Mathematicum},
pages = {1--20},
year = {2011},
volume = {123},
number = {1},
doi = {10.4064/cm123-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm123-1-1/}
}
TY - JOUR
AU - Irshaad Ahmed
AU - Georgi Eremiev Karadzhov
TI - Optimal embeddings of generalized homogeneous Sobolev spaces
JO - Colloquium Mathematicum
PY - 2011
SP - 1
EP - 20
VL - 123
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/cm123-1-1/
DO - 10.4064/cm123-1-1
LA - en
ID - 10_4064_cm123_1_1
ER -
%0 Journal Article
%A Irshaad Ahmed
%A Georgi Eremiev Karadzhov
%T Optimal embeddings of generalized homogeneous Sobolev spaces
%J Colloquium Mathematicum
%D 2011
%P 1-20
%V 123
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm123-1-1/
%R 10.4064/cm123-1-1
%G en
%F 10_4064_cm123_1_1
Irshaad Ahmed; Georgi Eremiev Karadzhov. Optimal embeddings of generalized homogeneous Sobolev spaces. Colloquium Mathematicum, Tome 123 (2011) no. 1, pp. 1-20. doi: 10.4064/cm123-1-1
