Weighted Hardy inequalities beyond Lipschitz domains
Lehrbäck, J. (2014). Weighted Hardy inequalities beyond Lipschitz domains. Proceedings of the American Mathematical Society, 142(5), 1705-1715. https://doi.org/10.1090/S0002-9939-2014-11904-6
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Proceedings of the American Mathematical SocietyAuthors
Date
2014Copyright
© 2014 American Mathematical Society. This is a final draft version of an article whose final and definitive form has been published by AMS. Published in this repository with the kind permission of the publisher.
It is a well-known fact that in a Lipschitz domain Ω ⊂ R
n
a p-Hardy inequality, with weight dist(x, ∂Ω)β
, holds for all u ∈ C
∞0 (Ω)
whenever β < p − 1. We show that actually the same is true under
the sole assumption that the boundary of the domain satisfies a uniform
density condition with the exponent λ = n − 1. Corresponding results
also hold for smaller exponents, and, in fact, our methods work in general
metric spaces satisfying standard structural assumptions.
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