Geodesic
An interpolation result for A_1 weights with applications to fractional Poincaré inequalities
Irene Drelichman1
1 Universidad Nacional de La Plata, CMaLP, Departamento de Matemática
Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 319–332.

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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.
DOI : 10.54330/afm.145700

Irene Drelichman 1

1 Universidad Nacional de La Plata, CMaLP, Departamento de Matemática 
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Irene Drelichman. An interpolation result for A_1 weights with applications  to fractional Poincaré inequalities. Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 319–332. doi : 10.54330/afm.145700. http://geodesic.mathdoc.fr/articles/10.54330/afm.145700/

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