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arXiv · 1908.11641

Boundedness of multilinear pseudo-differential operators of $S_{0,0}$-type in $L^2$-based amalgam spaces

Tomoya Kato·Akihiko Miyachi·Naohito Tomita
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Abstract

We consider the multilinear pseudo-differential operators with symbols in a generalized $S_{0,0}$-type class and prove the boundedness of the operators from $(L^2,\ell^{q_1}) \times \dots \times (L^2,\ell^{q_N})$ to $(L^2,\ell^{r})$, where $(L^2, \ell^{q})$ denotes the $L^2$-based amalgam space. This extends the previous result by the same authors, which treated the bilinear pseudo-differential operators and gave the $L^2 \times L^2 $ to $(L^2, \ell^{1})$ boundedness.

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Tomoya Kato, Akihiko Miyachi, Naohito Tomita. 2019-08-30. Boundedness of multilinear pseudo-differential operators of $S_{0,0}$-type in $L^2$-based amalgam spaces. https://arxiv.org/abs/1908.11641

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