TY - JOUR
AU - Ihnatsyeva, Lizaveta
AU - Lehrbäck, Juha
AU - Vähäkangas, Antti V.
PY - 2022/12/04
Y2 - 2023/01/30
TI - Hardy-Sobolev inequalities and weighted capacities in metric spaces
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 128
IS - 3
SE - Articles
DO - 10.7146/math.scand.a-133257
UR - https://www.mscand.dk/article/view/133257
SP -
AB - <p>Let $\Omega$ be an open set in a metric measure space $X$. Our main result gives an equivalence between the validity of a weighted Hardy–Sobolev inequality in $\Omega$ and quasiadditivity of a weighted capacity with respect to Whitney covers of $\Omega$. Important ingredients in the proof include the use of a discrete convolution as a capacity test function and a Maz'ya type characterization of weighted Hardy–Sobolev inequalities.</p>
ER -