Szego Seminar: Extrapolation Extravaganza!

Abstract: Tired of checking that your operators are bounded on all of L^p? Wish you could just work on L^2? Then extrapolation is what you need! Determining when operators are bounded between certain Banach spaces is a fundamental question in harmonic analysis. It has important applications to other areas such as PDEs, complex analysis, etc. In this talk we will investigate weighted norm inequalities for the Hardy-Littlewood maximal operator. We will discuss the Ap condition for weights and give a sketch as to why it’s the right condition for the maximal operator to satisfy weighted bounds. Finally, we’ll use this result to prove a powerful extrapolation result, which in the words of Antonio Córdoba, shows “there is no L^p, only weighted L^2”.