An integral inequality with applications

Author:
M. A. Leckband

Journal:
Trans. Amer. Math. Soc. **283** (1984), 157-168

MSC:
Primary 26D20; Secondary 26A51

DOI:
https://doi.org/10.1090/S0002-9947-1984-0735413-7

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:
https://doi.org/10.1090/S0002-9947-1984-0735413-7

Article copyright:
© Copyright 1984
American Mathematical Society