Kakeya sets and applications to analysis

Brian David Vasquez Campos

**Keywords:**Kakeya sets | Fefferman's theorem | Bochner-Riesz multipliers

This dissertation presents the Kakeya sets and the relationship with analysis. The construction discussed is a variant of the one originally given by Besicovitch

which is simple but it is surprising the connection with problems in other areas seemingly unrelated, the Fefferman theorem is treated as a disproof of the disk conjecture,this is an example of use the Kakeya construction to obtain an analysis result. The abstract definition of multiplier give us certain important results that we use to study the Bochner-Riesz multipliers as example of operators with kernel less singular that the ball multiplier and obtain a critical value for the boundedness of them,