What are non-tagential limits? I'm reading this article where they use a set of functions, $H^{\infty}$, defined like this "Let $H^{\infty }$ be the closed subalgebra of $L^{\infty }({\mathbb R})$ that consists of all functions being non-tangential limits on ${\mathbb R}$ of bounded analytic functions on the upper half plane." The thing is I don't know what is reffered as a non tangential limit. Please help. 

If $x_n\to x$, we say that $(x_n)$ is a non-tangential sequence in the upper half plane if $\inf_{n > 0}\text{Im}(x_n-x)/\text{Re}(x_n-x) > 0$.  So $f(x_n)$ converges non-tangentially to $y$ if $f(x_n)$ converges to $y$, and $(x_n)$ is a non-tangential sequence.
So $x_n = (a+ib)/n$ for $b>0$ is non-tangential, but $x_n = \frac1n + i\frac1{n^2}$ is not non-tangential.
http://demonstrations.wolfram.com/StolzAngle/ illustrates the concept (because non-tangential convergence is equivalent to convergence in so called Stolz domains).
