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 
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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/