Geodesic
Orlicz-Sobolev inequalities and the doubling condition
Lyudmila Korobenko1
1 Reed College, Mathematics Department
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 153-161

Voir la notice de l'article provenant de la source Journal.fi

In [12] it has been shown that a $(p,q)$ Sobolev inequality with $p>q$ implies the doubling condition on the underlying measure. We show that even weaker Orlicz-Sobolev inequalities, where the gain on the left-hand side is smaller than any power bump, imply doubling. Moreover, we derive a condition on the quantity that should replace the radius on the righ-hand side (which we call `superradius'), that is necessary to ensure that the space can support the Orlicz-Sobolev inequality and simultaneously be non-doubling.  
Keywords: Orlicz spaces, Sobolev inequality, metric measure spaces, doubling condition, non-doubling measure

Lyudmila Korobenko 1

1 Reed College, Mathematics Department 
@article{AFM_2021_46_1_a8,
     author = {Lyudmila Korobenko},
     title = {Orlicz-Sobolev inequalities and the doubling condition},
     journal = {Annales Fennici Mathematici},
     pages = {153--161},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a8/}
}
TY  - JOUR
AU  - Lyudmila Korobenko
TI  - Orlicz-Sobolev inequalities and the doubling condition
JO  - Annales Fennici Mathematici
PY  - 2021
SP  - 153
EP  - 161
VL  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a8/
LA  - en
ID  - AFM_2021_46_1_a8
ER  - 
%0 Journal Article
%A Lyudmila Korobenko
%T Orlicz-Sobolev inequalities and the doubling condition
%J Annales Fennici Mathematici
%D 2021
%P 153-161
%V 46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a8/
%G en
%F AFM_2021_46_1_a8
Lyudmila Korobenko. Orlicz-Sobolev inequalities and the doubling condition. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 153-161. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a8/