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