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Hardy's Inequality for W0 1,p-Functions on Riemannian Manifolds
Vladimir M. Miklyukov and Matti K. Vuorinen
Proceedings of the American Mathematical Society
Vol. 127, No. 9 (Sep., 1999), pp. 2745-2754
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/119576
Page Count: 10
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We prove that for every Riemannian manifold χ with the isoperimetric profile of particular type there holds an inequality of Hardy type for functions of the class W0 1,p(χ ). We also study manifolds satisfying Hardy's inequality and, in particular, we establish an estimate for the rate of growth of the weighted volume of the noncompact part of such a manifold.
Proceedings of the American Mathematical Society © 1999 American Mathematical Society