Sharp constants in exponential inequalities involving a general class of measures in domains Ω ⊂ Rn are exhibited in the limiting case of the Sobolev embedding theorem. A comprehensive approach is presented yielding, as special instances, trace inequalities on ∂Ω, on smooth submanifolds of Ω of arbitrary dimension, and also on fractal subsets of Ω, and recovering, in particular, the classical Moser-Trudinger inequality. © 2007 Elsevier Inc. All rights reserved.
Cianchi, A. (2008). Moser-Trudinger trace inequalities. Advances in Mathematics, 217(5), 2005–2044. https://doi.org/10.1016/j.aim.2007.09.007