Light PhD Seminar: Rubio de Francia square function: overview of some results

Title
Rubio de Francia square function: overview of some results

Abstract
The classical Littlewood-Paley theory states that the Lp norm of a function is
equivalent to the Lp norm of its Littlewood-Paley square function. This square function
is defined as the `2 norm of smooth (or rough) frequency projections to suitable dyadic
intervals. The Rubio de Francia square function is a generalisation of the Littlewood-
Paley square function, where we consider an arbitrary collection of disjoint intervals.
In this talk we will give an overview of some of the results by Rubio de Francia.
In particular, we will see that the Rubio de Francia square function is bounded from
Lp to Lp in the range 2   p < 1. To do that, first we will consider collections
of intervals where the intervals have the same length and later we will consider any
arbitrary collection of intervals.

Registration deadline: November 12th
Registration form: https://forms.gle/N4E1JQZuFyiAredt9