2021/01/07 by Renato Lucà, Lucà, Renato, Felipe Ponce-Vanegas +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2101.02495
openalex publication_date 2021/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with respect to the α-Hausdorff measure (α-a.e.). We extend to the fractal setting (α< n) a recent counterexample of Bourgain \citeBourgain2016, which is sharp in the Lebesque measure setting (α= n). In doing so we recover the necessary condition from \citezbMATH07036806 for pointwise convergence~α-a.e. and we extend it to the range n/2