Hardy-Sobolev inequalities and weighted capacities in metric spaces
نویسندگان
چکیده
Let $\Omega$ be an open set in a metric measure space $X$. Our main result gives equivalence between the validity of weighted Hardy–Sobolev inequality and quasiadditivity capacity with respect to Whitney covers $\Omega$. Important ingredients proof include use discrete convolution as test function Maz'ya type characterization inequalities.
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ژورنال
عنوان ژورنال: Mathematica Scandinavica
سال: 2022
ISSN: ['0025-5521', '1903-1807']
DOI: https://doi.org/10.7146/math.scand.a-133257