A note on the almost everywhere convergence to initial data for some evolution equations
Analysis of PDEs
2013-05-23 v2 Classical Analysis and ODEs
Functional Analysis
Abstract
The weighted Lebesgue spaces of initial data for which almost everywhere convergence of the heat equation holds was only very recently characterized. In this note we show that the same weighted space of initial data is optimal for the heat--diffusion parabolic equations involving the harmonic oscillator and the Ornstein--Uhlenbeck operator.
Keywords
Cite
@article{arxiv.1206.4530,
title = {A note on the almost everywhere convergence to initial data for some evolution equations},
author = {I. Abu-Falahah and P. R. Stinga and J. L. Torrea},
journal= {arXiv preprint arXiv:1206.4530},
year = {2013}
}
Comments
6 pages. To appear in Potential Analysis