%0 Journal Article
%T Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings
%A Evgeniy Pustylnik
%J Journal of Function Spaces and Applications
%D 2005
%I Hindawi Publishing Corporation
%R 10.1155/2005/254184
%X Let Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x∈Ω⊂ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A=Lφ,E, B=Lψ,E, giving some optimal (or rather sharp) relations between parameter-functions φ(t) and ψ(t) and new results for embeddings of Orlicz-Sobolev spaces.
%U http://www.hindawi.com/journals/jfsa/2005/254184/abs/