Nonlocal Schr\"odinger equations in metric measure spaces

TL;DR

This paper investigates the pointwise convergence of solutions to nonlocal dyadic Schr"odinger equations on metric measure spaces, establishing almost everywhere convergence for initial data in a dyadic Besov space.

Contribution

It proves a.e. convergence of solutions in a nonlocal Schr"odinger setting on spaces of homogeneous type, extending classical results to a dyadic and metric measure space context.

Findings

Almost everywhere convergence for initial data in dyadic Besov spaces

Extension of Schr"odinger equation analysis to metric measure spaces

New convergence results for nonlocal dyadic Schr"odinger equations

Abstract

In this note we consider the pointwise convergence to the initial data for the solutions of some nonlocal dyadic Schr\"odinger equations on spaces of homogeneous type. We prove the a.e. convergence when the initial data belongs to a dyadic version of an $L^2$ based Besov space.