3 papers
math.AP2026
Global quadratic estimates for degenerate elliptic operators on cylinders
Gianmarco Brocchi, Andreas Rosén
On -dimensional cylinders , with a closed manifold as base and large scale dimension , we prove quadratic estimates in weighted…
math.AP2024
The metric for matrix degenerate Kato square root operators
Gianmarco Brocchi, Andreas Rosén
We prove a Kato square root estimate with anisotropically degenerate matrix coefficients. We do so by doing the harmonic analysis using an auxiliary Riemannian metric adapted to th…
math.CA2020
A sparse quadratic theorem
Gianmarco Brocchi
We show that any Littlewood--Paley square function satisfying a minimal local testing condition is dominated by a sparse form, \begin{equation*} \langle (Sf)^2,g \rangle\le C \…