6533b82bfe1ef96bd128cdd0

RESEARCH PRODUCT

On improved fractional Sobolev–Poincaré inequalities

Bartłomiej DydaLizaveta IhnatsyevaAntti V. Vähäkangas

subject

Hölder's inequalityKantorovich inequalityPure mathematicsYoung's inequalityBernoulli's inequalityGeneral Mathematics010102 general mathematicsMathematical analysisMinkowski inequality01 natural sciences010101 applied mathematicsLog sum inequalityRearrangement inequality0101 mathematicsCauchy–Schwarz inequalityMathematics

description

We study a certain improved fractional Sobolev–Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev–Poincaré inequality. We prove the equivalence of the corresponding weak and strong type inequalities; this leads to a simple proof of a strong type inequality on John domains. We also give necessary conditions for the validity of an improved fractional Sobolev–Poincaré inequality, in particular, we show that a domain of finite measure, satisfying this inequality and a ‘separation property’, is a John domain.

yearjournalcountryeditionlanguage
2016-10-01Arkiv för Matematik
https://doi.org/10.1007/s11512-015-0227-x