To deal with $Tf$, we note that ...... [= Regarding $\langle$Concerning$\rangle$ $Tf$, we note]
Although  deals mainly with the unit disc, most proofs are so constructed that they apply to more general situations.
It became clear that the Riemann integral should be replaced by some other type of integral, better suited for dealing with limit processes.
A survey of the research on $f_n(x,y)$ up to 1970 (most of it dealing with the case $n=1$) was given in .
Instead of dealing with lines one by one, we deal with collections of lines simultaneously.
This topic has been dealt with by many authors.