Analysis & Applications Seminar
Calderón–Zygmund theory on Damek–Ricci spaces
Speaker: Martina Bernardelli (Politecnico di Torino)Date: Friday, 16 October 2026 - 11:30Place: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
Calderón--Zygmund theory provides a fundamental framework for the study of singular integral operators. Building on the approach of Hebisch and Steger for a class of Lie groups of exponential growth, and on the recent abstract framework of Conde Alonso, Martini and Vallarino, we show that Damek--Ricci spaces \(S=N\rtimes\mathbb{R}\), with \(N\) an \(H\)-type group, fit into this setting. We build a nested system of admissible sets on \(S\): parallelepipeds \(\mathcal Q\times I\), where \(\mathcal Q\) is a cube on \(N\) coming from Strichartz's self-similar tiling. This yields the associated Calderón--Zygmund theory on \(S\), including endpoint estimates for singular integral operators. In particular, the Riesz transforms are bounded from the atomic Hardy space \(H^1\) associated with these admissible sets into \(L^1\), while their adjoints are not. This seminar is based on a joint work with Jie Liu and Alessio Martini.
