Seminario Análisis y Aplicaciones
Sharp L^2-bounds for directional maximal functions along arbitrary directions in R^3
Ponente: Ioannis Parissis (UPV)Fecha: viernes 21 de noviembre de 2025 - 11:30Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
I will present a sharp (up to ε losses) \(L^2\)-bound for the directional maximal function associated with N arbitrary directions in \(\mathbb{R}^3\). The main ingredient is a critical and essentially optimal \(L^2\) estimate for N directions lying on algebraic curves in \(\mathbb{R}^3\), combined with a polynomial partition of the set of directions. The curve estimate is the main subject of the talk. It is obtained through a geometric analysis of the corresponding Fourier multipliers, which leads to an almost-orthogonality principle that can be applied recursively. Certain algebraic-geometric obstructions must be handled somewhat separately from the analysis; these are resolved using algebraic preparation results together with a suitable Bernstein–Remez inequality for holomorphic algebraic functions.
This talk reports on joint work with F. Di Plinio (Napoli Federico II).
