Explicit formulas for optimal rearrangement-invariant norms in Sobolev imbedding inequalities

Abstract

Imbeddings of a Sobolev space into a rearrangement-invariant space are studied. The optimal range norms are explicitly described.

Keywords

• Sobolev imbeddings
• rearrangement-invariant
• norms
• explicit formulas
• optimal range norms
• optimal domain norms