An interpolation result for A_1 weights with applications to fractional Poincaré inequalities
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.
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
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author = {Irene Drelichman},
title = {An interpolation result for {A_1} weights with applications to fractional {Poincar\'e} inequalities},
journal = {Annales Fennici Mathematici},
pages = {319{\textendash}332--319{\textendash}332},
year = {2024},
volume = {49},
number = {1},
doi = {10.54330/afm.145700},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.145700/}
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