Caltech/UCLA Joint Analysis Seminar

UCLA, MS 6627

 I will present some recent work concerning extremization in harmonic analysis. We will focus on the following question: Among functions f majorized by indicator functions 1 E 1E,which functions have maximal ratio ∥f ˆ ∥ q /|E| 1/p ‖f^‖q/|E|1/p? I will give some context for this question, and describe what is known so far. Then for exponents q∈(3,∞) q∈(3,∞) sufficiently close to even integers, we identify the maximizers and prove a quantitative stability theorem.