# Extrapolation for multilinear Muckenhoupt class of weights and applications

In this talk, I will introduce our recent progress on extrapolation theory. In the linear case, the extrapolation theory is well understood. However, in the multilinear case, the extrapolation was only known for product $A_p$ weights. The multilinear $A_{\vec P}$ weight, which was introduced in 2009, no extrapolation theory was known before. In this talk, I will give a full solution to this problem. As applications, we can improve the weighted estimates for the bilinear Hilbert transform, the multilinear Marcinkiewicz-Zygmund inequality etc. Endpoint cases are also provided. This talk is based on joint work with José María Martell and Sheldy Ombrosi, and joint work with Henri Martikainen, José María Martell, Sheldy Ombrosi and Emil Vuorinen.

This talk is part of the Analysis Seminar series.