Weighted Fractional Sobolev-Poincaré Inequalities in Irregular Domains
We study weighted fractional Sobolev-Poincaré inequalities in irregular domains.The weights considered here are distances to the boundary to certain powers,and the domains are the so-called s-John domains and β-Hölder domains.Our main results extend that of Hajlasz-Koskela[J.Lond.Math.Soc.,1998,58(2):425-450]from the classical weighted Sobolev-Poincaré inequality to its fractional counter-part and Guo[Chin.Ann.Math.,2017,38B(3):839-856]from the fractional Sobolev-Poincaré inequality to its weighted case.
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