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Boundedness of bilinear pseudo‐differential operators with BS0,0m$BS^{m}_{0,0}$ symbols on Sobolev spaces

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  • Naoto Shida

Abstract

In this paper, bilinear pseudo‐differential operators with symbols in the bilinear Hörmander class BS0,0m$BS^m_{0,0}$ are considered. In particular, the boundedness of these operators on Sobolev spaces is established. Our main result is proved by using symbolic calculus and the boundedness of those operators with certain S0, 0‐type symbols on Lebesgue spaces.

Suggested Citation

  • Naoto Shida, 2023. "Boundedness of bilinear pseudo‐differential operators with BS0,0m$BS^{m}_{0,0}$ symbols on Sobolev spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 296(10), pages 4806-4834, October.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:10:p:4806-4834
    DOI: 10.1002/mana.202200169
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