Weighted fractional Sobolev-Poincaré inequalities in irregular domains

Abstract

In this paper, we study weighted fractional Sobolev-Poincaré inequalities for 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 $\beta$-Hölder domains. Our main results extend that of Hajlasz-Koskela [J. Lond. Math. Soc. 1998] from the classical weighted Sobolev-Poincaré inequality to its fractional counter-part and Guo [Chin. Ann. Math. 2017] from the frational Sobolev-Poincaré inequality to its weighted case.

Accepted for publication in the journal "Acta Mathematica Sinica, Chinese Series"