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A Note on the Almost Everywhere Convergence to Initial Data for Some Evolution Equations |
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| Authors: | Ibraheem Abu-Falahah Pablo Raúl Stinga José L Torrea |
| Institution: | 1. Department of Mathematics, The Hashemite University, Zarqa, Jordan 2. Departament of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, TX, 78712-1202, USA 3. Departamento de Matemáticas and ICMAT-CSIC-UAM-UCM-UC3M, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain |
| 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. |
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