函数空间上的二重外推法及其应用

IF 0.8 3区 数学 Q2 MATHEMATICS
Mingming Cao, Andrea Olivo
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引用次数: 0

摘要

本文致力于研究 Rubio de Francia 关于一般函数空间的外推法理论。我们介绍了端点外推法的结果,包括巴拿赫函数空间的 、 、 和外推法,以及模块空间的外推法。我们还介绍了利用外推法可以轻松获得的几种应用:各种算子的局部衰减估计、可用于证明一些已知尖锐不等式的 Coifman-Fefferman 不等式、许多算子的 Muckenhoupt-Wheeden 和 Sawyer 猜想,这些猜想超出了 Calderón-Zygmund 算子的范围。最后,我们得到了加权巴拿赫函数空间上 Littlewood-Paley 算子和傅里叶积分算子的两重不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Two-weight extrapolation on function spaces and applications

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 $A_1$ , A p $A_p$ , and A $A_\infty$ 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 $A_1$ inequalities, Muckenhoupt–Wheeden and Sawyer's conjectures are also presented for many operators, which go beyond Calderón–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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来源期刊
CiteScore
1.50
自引率
0.00%
发文量
157
审稿时长
4-8 weeks
期刊介绍: Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index
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