Improved fractional Poincaré type inequalities on John domains

Published 27 Feb 2019 in math.CA | (1902.10578v1)

Abstract: We obtain improved fractional Poincar\'e inequalities in John domains of a metric space $(X, d)$ endowed with a doubling measure $\mu$ under some mild regularity conditions on the measure $\mu$. We also give sufficient conditions on a bounded domain to support fractional Poincar\'e type inequalities in this setting.

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