Resumen en inglés

In the present work we make use of one of the most important operators in Fourier analysis, which receives the name of Fourier Transform and we show some properties. Then, we extend the Fourier transform operator to continuous linear functionals defined on test spaces, whose functionals are called distributions, we will focus our study on the particular case of the so-called tempered distributions, since through these distributions and the spaces L p we will define our objective, which are the socalled Sobolev spaces, and together with this we will demonstrate some of its most important properties.