Analysis Seminar: Olli Tapiola
Title: What is so difficult about high-dimensional one-sided Muckenhoupt theory?
Abstract: A classical result of Muckenhoupt says that the Hardy-Littlewood maximal operator is bounded from the weighted L^p space to itself if and only if the weight satisfies the so called A_p condition. This result has been generalized and sharpened over and over again in the literature but for the one-sided Hardy-Littlewood maximal operator the result is known only in dimension 1. Although the one-sided theory may seem like simple and straightforward generalization of the original theory, the one-sided nature of the questions actually makes most of known tools useless or hard to use. In this talk, we discuss what is known about this high-dimensional theory and why it is so difficult.
Contact Name: Cristina Pereyra