Sharp Sobolev embeddings and related Hardy inequalities : The critical case

Preprint series: 99-05, Analysis

The paper is published: Math.Nachr., 207, 79-92, 1999.

MSC:
46E35 Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems

Abstract: The paper deals with sharp embeddings of the Sobolev spaces $H^s_p(R^n)$ and the spaces $B^s_{pp}(R^n)$ into rearrangement-invariant spaces and related Hardy inequalities. Here $1<p<\infty$ and $s=n/p$.

Keywords: function spaces, embeddings, Hardy inequalities, rearrangement