Orlicz Sobolev Inequalities and the Doubling Condition

Lyudmila Korobenko

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arXiv · 1906.04088

Orlicz Sobolev Inequalities and the Doubling Condition

Lyudmila Korobenko

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Abstract

In [12] it has been shown that $(p,q)$ 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.

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BibTeX RIS

Lyudmila Korobenko. 2019-06-06. Orlicz Sobolev Inequalities and the Doubling Condition. https://arxiv.org/abs/1906.04088

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