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arXiv · 2101.06920

Two-weight extrapolation on function spaces and applications

Mingming Cao·Andrea Olivo
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Abstract

This paper is devoted to studying the extrapolation theory of Rubio de Francia on general function spaces. We present endpoint extrapolation results including $A_1$, $A_p$, and $A_\infty$ extrapolation in the context of Banach function spaces, and also on modular spaces. We also include several applications that can be easily obtained using extrapolation: local decay estimates for various operators, Coifman--Fefferman inequalities that can be used to show some known sharp $A_1$ inequalities, Muckenhoupt--Wheeden and Sawyer's conjectures are also presented for many operators, which go beyond Calder\'{o}n--Zygmund operators. Finally, we obtain two-weight inequalities for Littlewood--Paley operators and Fourier integral operators on weighted Banach function spaces.

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Mingming Cao, Andrea Olivo. 2021-01-18. Two-weight extrapolation on function spaces and applications. https://doi.org/10.1002/mana.202300120

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