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

TL;DR

This paper establishes the boundedness of multilinear pseudo-differential operators with $S_{0,0}$-type symbols on $L^2$-based amalgam spaces, extending previous bilinear results to multilinear cases.

Contribution

It generalizes previous bilinear boundedness results to multilinear operators with symbols in a generalized $S_{0,0}$ class on amalgam spaces.

Findings

Boundedness of multilinear pseudo-differential operators on amalgam spaces.

Extension from bilinear to multilinear operators.

Generalization to a broader class of symbols.

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.