Endpoint estimates for Rubio de Francia operators

Carro, María; Domingo-Salazar, Carlos

doi:10.1090/tran/7328

Endpoint estimates for Rubio de Francia operators
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by María J. Carro and Carlos Domingo-Salazar PDF

Trans. Amer. Math. Soc. 371 (2019), 1621-1648 Request permission

Abstract:

The extrapolation theory of Rubio de Francia provides a tool to obtain $A_p$ weighted estimates on $L^p$ spaces for every $1<p<\infty$, starting from information at a single $1<p_0<\infty$. However, the endpoint case $p=1$ cannot be reached in general. Classical extrapolation arguments in the sense of Yano can be added to this setting to deduce results close to $L^1$ without weights. In this paper, we present different approaches that produce endpoint estimates with respect to the whole $A_1$ class. We give applications to the Carleson operator and maximally modulated singular integrals among others.

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