Orlicz-Sobolev inequalities and the doubling condition

Kirjoittajat

  • Lyudmila Korobenko Reed College, Mathematics Department

Avainsanat:

Orlicz spaces, Sobolev inequality, metric measure spaces, doubling condition, non-doubling measure

Abstrakti

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.

 

Osasto
Articles

Julkaistu

2021-06-21

Viittaaminen

Korobenko, L. (2021). Orlicz-Sobolev inequalities and the doubling condition. Annales Fennici Mathematici, 46(1), 153–161. Noudettu osoitteesta https://afm.journal.fi/article/view/109517