Endpoint multilinear restricted weak‐type extrapolation theorem

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 for certain bi‐sublinear maximal functions associated with the study of return time theorems in ergodic theory.