$W^{1,p}-$regularity on the boundary for solution of Laplace equation with Robin boundary condition

Question

I came across with the attached paper and here is the part that I try to understand.

If the non-tangential maximal function of $\nabla u$, i.e $(\nabla u)^*$, belongs in $L^p(\partial \Omega)$, then can one derive that $u \in W^{1,p}(\partial \Omega)$?

I 'm not familiar with the term non-tangential maximal function, hence I have troubles understanding the result of the authors in this paper. I would really appreciate it if someone could enlighten me with this and in addition provide some good reference for the regularity of solutions to the Laplace equation with Robin boundary condition.

Thanks a lot in advance for your time!