Orlicz Sobolev Inequalities and the Doubling Condition

2019/06/06 by Korobenko, Lyudmila · 2 citations
#30L99 #31E05 #35B65 #35J60 #35J70 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.04088

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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• Logarithmic double phase embeddings with variable exponents: Necessary and Sufficient Conditions
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