An interpolation result for A_1 weights with applications to fractional Poincaré inequalities
Abstrakti
We characterize the real interpolation space between weighted \(L^1\) and \(W^{1,1}\) spaces on arbitrary domains different from \(\mathbb{R}^n\), when the weights are positive powers of the distance to the boundary multiplied by an \(A_1\) weight. As an application of this result we obtain weighted fractional Poincaré inequalities with sharp dependence on the fractional parameter \(s\) (for \(s\) close to 1) and show that they are equivalent to a weighted Poincaré inequality for the gradient.Viittaaminen
Drelichman, I. (2024). An interpolation result for A_1 weights with applications to fractional Poincaré inequalities. Annales Fennici Mathematici, 49(1), 319–332. https://doi.org/10.54330/afm.145700
Copyright (c) 2024 Annales Fennici Mathematici
![Creative Commons License](http://i.creativecommons.org/l/by-nc/4.0/88x31.png)
Tämä työ on lisensoitu Creative Commons Nimeä-EiKaupallinen 4.0 Kansainvälinen Julkinen -lisenssillä.