Ph.D. Public Lecture (Math) - Alejandro Santacruz Hidalgo

A Calderón couple of Banach spaces related to decreasing functions

Abstract:

Given a compatible couple of Banach spaces, the description of all possible interpolation spaces is a fundamental question in interpolation theory. For Calderón couples it is possible to answer this question. We will study a pair of Banach spaces which are modified versions of L^1 and L^\infty on the half-line. First, we will introduce the relevant definitions and tools such as interpolation spaces and the K-method of interpolation. Then, we will present a result by Lesnik which shows that our pair of spaces forms a Calderón couple.