Startseite Mathematik Bi-parameter and bilinear Calderón–Vaillancourt theorem with critical order
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Bi-parameter and bilinear Calderón–Vaillancourt theorem with critical order

  • Jiao Chen , Liang Huang und Guozhen Lu EMAIL logo
Veröffentlicht/Copyright: 31. Januar 2024

Abstract

In this paper, we establish the sharp Calderón–Vaillancourt theorem on L p spaces for bi-parameter and bilinear pseudo-differential operators with symbols of critical order by deriving a sufficient and necessary condition on its symbol. This sharpens the result of [G. Lu and L. Zhang, Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order, Forum Math. 28 2016, 6, 1087–1094] which was only proved for symbols of subcritical order.

MSC 2020: 42B15; 42B25

Communicated by Christopher D. Sogge


Award Identifier / Grant number: 2022JQ-055

Funding statement: The second author is supported by the Natural Science Foundation of Shaanxi Province (Grant No. 2022JQ-055).

Acknowledgements

The authors thanks the anonymous referee for valuable comments which improve its exposition of the paper.

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Received: 2023-12-12
Published Online: 2024-01-31
Published in Print: 2024-09-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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