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

Steve Hudson, Mark Leckband
1999 Proceedings of the American Mathematical Society  
This paper generalizes an inequality of Moser from the case that ∇u is in the Lebesgue space L n to certain subspaces, namely the Lorentz spaces L n,q , where 1 < q ≤ n. The conclusion is that exp(αu 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 α is given and it is also shown that no larger value of α works.
doi:10.1090/s0002-9939-99-05147-3 fatcat:bo4njue3vffadplmbrob2xm6ve