Regularity and pointwise convergence of solutions of the Schrödinger operator with radial initial data on Damek-Ricci spaces

Authors

• Utsav Dewan, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Annali Di Matematica Pura Ed Applicata

Abstract

One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson’s problem: determining the optimal regularity of the initial condition f of the Schrödinger equation given by (Formula presented.) in terms of the index α such that f belongs to the inhomogeneous Sobolev space H^α(Rⁿ), so that the solution of the Schrödinger operator u converges pointwise to f, limt→0+u(x,t)=f(x), almost everywhere. In this article, we consider the Carleson’s problem for the Schrödinger equation with radial initial data on Damek-Ricci spaces and obtain the sharp bound up to the endpoint α≥1/4, which agrees with the classical Euclidean case.

First Page

1161

Last Page

1182

DOI

10.1007/s10231-024-01523-2

Publication Date

6-1-2025

Recommended Citation

Dewan, Utsav, "Regularity and pointwise convergence of solutions of the Schrödinger operator with radial initial data on Damek-Ricci spaces" (2025). Journal Articles. 5552.
https://digitalcommons.isical.ac.in/journal-articles/5552