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A Note on the Almost Everywhere Convergence to Initial Data for Some Evolution Equations

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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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Authors and Affiliations

  1. Department of Mathematics, The Hashemite University, Zarqa, Jordan

    Ibraheem Abu-Falahah

  2. Departament of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, TX, 78712-1202, USA

    Pablo Raúl Stinga

  3. Departamento de Matemáticas and ICMAT-CSIC-UAM-UCM-UC3M, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    José L. Torrea

Authors
  1. Ibraheem Abu-Falahah
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  2. Pablo Raúl Stinga
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  3. José L. Torrea
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Corresponding author

Correspondence to José L. Torrea.

Additional information

Research partially supported by grant MTM2011-28149-C02-01 from Gobierno de España.

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Abu-Falahah, I., Stinga, P.R. & Torrea, J.L. A Note on the Almost Everywhere Convergence to Initial Data for Some Evolution Equations. Potential Anal 40, 195–202 (2014). https://doi.org/10.1007/s11118-013-9351-z

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  • DOI: https://doi.org/10.1007/s11118-013-9351-z

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