Abstract
AbstractOur main result is a weighted fractional Poincaré–Sobolev inequality improving the celebrated estimate by Bourgain–Brezis–Mironescu. This also yields an improvement of the classical Meyers–Ziemer theorem in several ways. The proof is based on a fractional isoperimetric inequality and is new even in the non-weighted setting. We also extend the celebrated Poincaré–Sobolev estimate with $$A_p$$
A
p
weights of Fabes–Kenig–Serapioni by means of a fractional type result in the spirit of Bourgain–Brezis–Mironescu. Examples are given to show that the corresponding $$L^p$$
L
p
-versions of weighted Poincaré inequalities do not hold for $$p>1$$
p
>
1
.
Funder
Magnus Ehrnroothin Sääiö
Spanish Goverment
Basque Goverment
Basque Government
BCAM Severo Ochoa accreditation
European Union’s Horizon 2020 research and innovation programme
Publisher
Springer Science and Business Media LLC
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