Abstract
This article discusses some smoothing estimates of the initial value problem for dispersive equations with constant coefficients. In particular, it is shown that a certain condition for the principal part of the symbol (see the assumption (1.3) below, which is equivalent to the one “of principal type” in the paper by Ben-Artzi and Devinatz [2]) is necessary and sufficient for the maximal smoothing in space-time.
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Dedicated to Professor Norio Shimakura
The author was supported in part by Grant-in-Aid for Scientific Research, Ministry of Education, Culture, Sports, Science and Technology, Japan (No. 13640187).
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Hoshiro, T. Decay and regularity for dispersive equations with constant coefficients. J. Anal. Math. 91, 211–230 (2003). https://doi.org/10.1007/BF02788788
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DOI: https://doi.org/10.1007/BF02788788