Talk Abstracts

Function spaces used in harmonic analysis can typically be characterised using Littlewood-Paley or wavelet decompositions. These characterisations can be seen as embeddings of function spaces over physical space into function spaces over phase space. From this perspective, one can design function spaces associated with any wave packet transform that lifts functions into phase space. In this talk, I'll describe such spaces associated with anisotropic lifts that capture crucial features of wave equations.

This includes connections with decoupling theory and local smoothing, and methods to solve wave equations with rough coefficients. Based on joint works with Dorothee Frey, Andrew Hassell, Jan Rozendaal, and Po Lam Yung.