Multilinear multiplier theorems and their applications to the Jacobian and the Hessian determinant

TL;DR

This paper extends multilinear multiplier theorems, providing new variants and examples, with applications to defining Jacobian and Hessian determinants in the distributional framework.

Contribution

It introduces new variants of the multilinear multiplier theorem and applies them to the distributional definitions of Jacobian and Hessian determinants.

Findings

New variants of multilinear multiplier theorems established.

Examples not covered by existing theories are presented.

Applications to distributional Jacobian and Hessian determinants.

Abstract

We establish several variants of the multilinear multiplier theorem of Coifman and Meyer. We also present examples that are not covered by existing theories. Our motivation comes from applications to the definition of the Jacobian and Hessian determinant in the distributional sense.