On Lp-L1 estimates of logarithmic-type in Hardy-Sobolev spaces of the disk and the annulus

The aim of this paper is to prove some optimal estimates of logarithmic-type in Hardy-Sobolev spaces H1,p, 1≤p≤∞, of both the unit disk and the annulus. These estimates extend those previously established by Baratchart and Zerner in the Hardy-Sobolev space H1,2 of the unit disk and by Chaabane and the first author of the paper in the case of the spaces H1,∞ of the unit disk and of the annulus.