SEMINARIO DE ANÁLISIS COMPLEJO (COMPLEX ANALYSIS SEMINAR)

An extremal problem for Hp

Sarah May INSTANES
NTNU, Trondheim, Norway

Wednesday, October 2, 2024 at 15:30
Room 520, Module 17, Department of Mathematics,

Universidad Autónoma de Madrid (Autonomous University of Madrid)

Abstract:
For 0 < p ≤∞, let Hp denote the classical Hardy space of the unit disc. We consider
the extremal problem of maximizing the modulus of the kth Taylor coefficient of
a function f in Hp which satisfies ∥f ∥Hp ≤ 1 and f (0) = t for some 0 ≤ t ≤ 1. In
particular, we provide a complete solution to this problem for k = 1 and 0 < p < 1.
We also study F. Wiener’s trick, which plays a crucial role in various coefficientrelated
extremal problems for Hardy spaces. This is joint work with Ole Fredrik
Brevig and Sigrid Grepstad.