Fatou’s Theorem; its contribution to harmonic analysis

The objective of this article is to see how Fatou’s theorem, given at the beginning of the 20th century, motivated new developments in harmonic analysis and partial differential equations in the second half of that century. In this writing we give a brief tour of some of the contributions given by distinguished analysis and in this way our interest is to make such progress known in Peru and thus contribute to the development of this beautiful branch of mathematical analysis, which we believe is almost unknown in our country. In particular we have paid some attention to the work of Jerison - Kenig [1] because such work contains an overview that helps meet our objective.