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

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

In this paper, bilinear pseudo‐differential operators with symbols in the bilinear Hörmander class 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 cert...

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Veröffentlicht in:Mathematische Nachrichten 2023-10, Vol.296 (10), p.4806-4834
1. Verfasser: Shida, Naoto
Format: Artikel
Sprache:eng
Schlagworte:
Differential equations
Operators (mathematics)
Sobolev space
Symbols
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Zusammenfassung:In this paper, bilinear pseudo‐differential operators with symbols in the bilinear Hörmander class 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 S 0, 0 ‐type symbols on Lebesgue spaces.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202200169