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April, 2021 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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J. Math. Soc. Japan 73(2): 351-388 (April, 2021). DOI: 10.2969/jmsj/83468346

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 $(L^2, \ell^{q_1}) \times \cdots \times (L^2, \ell^{q_{N}})$ 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.

Funding Statement

This work was supported by JSPS KAKENHI Grant Numbers JP17J00359 (Kato), JP16H03943 (Miyachi), and JP16K05201 (Tomita).

Citation

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Tomoya KATO. Akihiko MIYACHI. Naohito TOMITA. "Boundedness of multilinear pseudo-differential operators of $S_{0,0}$-type in $L^2$-based amalgam spaces." J. Math. Soc. Japan 73 (2) 351 - 388, April, 2021. https://doi.org/10.2969/jmsj/83468346

Information

Received: 8 October 2019; Published: April, 2021
First available in Project Euclid: 7 October 2020

Digital Object Identifier: 10.2969/jmsj/83468346

Subjects:
Primary: 35S05
Secondary: 42B15, 42B35

Rights: Copyright ©2021 Mathematical Society of Japan

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Vol.73 • No. 2 • April, 2021
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