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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An integral inequality with applications


Author: M. A. Leckband
Journal: Trans. Amer. Math. Soc. 283 (1984), 157-168
MSC: Primary 26D20; Secondary 26A51
MathSciNet review: 735413
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Abstract: Using a technical integral inequality, J. Moser proved a sharp result on exponential integrability of a certain space of Sobolev functions. In this paper, we show that the integral inequality holds in a general setting using nonincreasing functions and a certain class of convex functions. We then apply the integral inequality to extend the above result by J. Moser to other spaces of Sobolev functions. A second application is given generalizing some different results by M. Jodeit.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0735413-7
PII: S 0002-9947(1984)0735413-7
Article copyright: © Copyright 1984 American Mathematical Society