Endpoint multilinear restricted weak type extrapolation theorem

TL;DR

This paper generalizes the endpoint extrapolation theorem for multilinear Muckenhoupt classes, introduces a limited range off-diagonal extrapolation theorem, and applies these results to endpoint estimates of bi-sublinear maximal functions in ergodic theory.

Contribution

It extends the endpoint extrapolation theorem to multilinear restricted weights and limited ranges, providing new tools for analysis in harmonic analysis and ergodic theory.

Findings

Generalized endpoint extrapolation theorem for multilinear restricted weights.

Introduced a new limited range, off-diagonal extrapolation theorem.

Proved endpoint estimates for bi-sublinear maximal functions.

Abstract

In this paper we present a generalization in the context of multilinear Muckenhoupt classes of the endpoint extrapolation theorem on restricted weights due to Carro, Grafakos and Soria. Moreover, our main result is obtained on limited ranges of boundedness and to this aim we introduce a new limited range, off-diagonal extrapolation theorem in the context of restricted weights. In addition, as one of the applications, we prove endpoint estimates of certain bi-sublinear maximal functions associated with the study of return time theorems in ergodic theory.