On the 𝐿^{∞}×𝐿^{∞}→𝐵𝑀𝑂 mapping property for certain bilinear pseudodifferential operators

Naibo, Virginia

doi:10.1090/proc12775

On the $L^\infty \times L^\infty \rightarrow BMO$ mapping property for certain bilinear pseudodifferential operators
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Proc. Amer. Math. Soc. 143 (2015), 5323-5336 Request permission

Abstract:

Boundedness from $L^\infty \times L^\infty$ into $BMO$ is proved for bilinear pseudodifferential operators with symbols in a range of bilinear Hörmander classes of critical order. This is achieved by means of new continuity results for bilinear operators with symbols in certain classes and a new pointwise inequality relating bilinear operators and maximal functions.

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