Sharp constants for Moser-type inequalities concerning embeddings into Zygmund spaces

Abstract

We give a Moser-type inequality for an embedding of the Orlicz-Sobolev spaces with the Young function having a logarithmic growth into Zygmund spaces. We also study the same problem for the embedding of the generalized Lorentz-Sobolev space embedded into the Zygmund spaces.

Keywords

• Orlicz-Sobolev spaces
• Lorentz-Sobolev spaces
• Trudinger embedding
• Moser-Trudinger inequality
• best constants