A generalization to the Hardy-Sobolev spaces H k , p of an L p - L 1 logarithmic type estimate

The main purpose of this article is to give a generalization of the logarithmictype estimate in the Hardy-Sobolev spaces H k , p ( G ); k ∈ N*, 1 ≤ p ≤ ∞ and G is the open unit disk or the annulus of the complex |space^C.