A note on the almost everywhere convergence to initial data for some evolution equations

2012/06/20 by Abu-Falahah, I., Stinga, P. R., Torrea, J. L. · 1 citation
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1206.4530

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.

Cited by

• Pointwise convergence to initial data of heat and Hermite-heat equations in Modulation Spaces

Related

• Pointwise convergence to initial data for some evolution equations on symmetric spaces
• A unified framework for pointwise convergence to the initial data of heat equations in metric measure spaces
• Pointwise convergence to initial data of heat and Hermite-heat equations in Modulation Spaces
• Parabolic Frequency on Gaussian Spaces and Unique Continuation
• On quasilinear parabolic evolution equations in weighted Lp-spaces II