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Transactions of the American Mathematical Society

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Uniformly fat sets


Author: John L. Lewis
Journal: Trans. Amer. Math. Soc. 308 (1988), 177-196
MSC: Primary 31B99
DOI: https://doi.org/10.1090/S0002-9947-1988-0946438-4
MathSciNet review: 946438
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Abstract: In this paper we study closed sets $ E$ which are "locally uniformly fat" with respect to a certain nonlinear Riesz capacity. We show that $ E$ is actually "locally uniformly fat" with respect to a weaker Riesz capacity. Two applications of this result are given. The first application is concerned with proving Sobolev-type inequalities in domains whose complements are uniformly fat. The second application is concerned with the Fekete points of $ E$.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0946438-4
Article copyright: © Copyright 1988 American Mathematical Society

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