Limited-Range Multilinear Off-Diagonal Extrapolation and Weighted Transference Principle

TL;DR

This paper develops a comprehensive multilinear off-diagonal extrapolation theory in mixed-norm Lebesgue spaces, allowing full range exponents and establishing a weighted transference principle, with new endpoint results even in Euclidean spaces.

Contribution

It introduces a novel limited-range, multilinear off-diagonal extrapolation framework with fully decoupled weight and space exponents, extending applicability and providing new endpoint insights.

Findings

Established full-range extrapolation results for mixed-norm Lebesgue spaces.

Derived new endpoint estimates in Euclidean spaces.

Proved a weighted transference principle for compact abelian groups.

Abstract

Multilinear $L^p$ extrapolation results are established in a limited-range, multilinear, and off-diagonal setting for mixed-norm Lebesgue spaces over $\sigma$-finite measure spaces. Integrability exponents are allowed in the full range $(0,\infty]$. We detach the exponents for the weight classes completely from the exponents for the initial and target spaces for the extrapolation except for the basic consistency condition. This enables to cover the full range $(0,\infty]$ for all integrability exponents and provides new insights into the dependency of the extrapolated bounds on the weight characteristic. Certain endpoint results are new even for $\mathbb{R}^d$. Additionally, in the setting of compact abelian groups, a weighted transference principle is established.