An exact estimate of the boundary behavior of functions from Hardy–Sobolev classes in the critical case

In the critical case $\alpha p=n$ functions from the Hardy-Sobolev spaces $H_\alpha^p(B^n)$ have a limit almost everywhere on the boundary along certain regions of exponential contact with the boundary. It is proved in the paper that the maximal operator associated with these regions is bounded as an operator from $H_\alpha^p(B^n)$ to $L^p(\partial B^n)$.