Sharp lower bounds for the periodic maximal Schrödinger operator in higher dimensions
Inbo Gottlieb Fenves, Jiahao Tan
Source abstract
We prove sharp lower bounds for the Schrödinger maximal function on the torus T^d for all dimensions d at least 2, and as a corollary obtain sharp regularity conditions for pointwise convergence of the periodic Schrödinger equation. Combined with sufficiency results established by Compaan-Lucá-Staffilani, this yields a full resolution of Carleson's problem up to endpoint for the periodic Schrödinger equation in all dimensions at least 2, and disproves the conjectured regularity condition of Miao-Yuan-Zhao, in contrast to the corresponding question in R^d. We also prove sharp estimates on the dimensions of divergence sets for the equation for high dimensional tori. Our approach uses complex multiplication on abelian varieties.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.