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

Naoto Shida

Mathematische Nachrichten, 2023, vol. 296, issue 10, 4806-4834

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.

Date: 2023
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https://doi.org/10.1002/mana.202200169

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