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Proceedings of the American Mathematical Society

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A sharp exponential inequality
for Lorentz-Sobolev spaces
on bounded domains


Authors: Steve Hudson and Mark Leckband
Journal: Proc. Amer. Math. Soc. 127 (1999), 2029-2033
MSC (1991): Primary 46E35; Secondary 46E30
DOI: https://doi.org/10.1090/S0002-9939-99-05147-3
Published electronically: February 26, 1999
MathSciNet review: 1643410
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Abstract: This paper generalizes an inequality of Moser from the case that $\nabla u$ is in the Lebesgue space $L^n$ to certain subspaces, namely the Lorentz spaces $L^{n,q}$, where $1<q\leq n$. The conclusion is that $\exp(\alpha u^p)$ is integrable, where $1/p+1/q=1$. This is a higher degree of integrability than in the Moser inequality when $q<n$. A formula for $\alpha$ is given and it is also shown that no larger value of $\alpha$ works.


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Additional Information

Steve Hudson
Affiliation: Department of Mathematics, Florida International University, University Park, Miami, Florida 33199
Email: hudsons@fiu.edu

Mark Leckband
Affiliation: Department of Mathematics, Florida International University, University Park, Miami, Florida 33199
Email: leckband@fiu.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05147-3
Keywords: Sobolev imbedding theorem, Moser's inequality, Lorentz space
Received by editor(s): September 16, 1997
Published electronically: February 26, 1999
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society