关于Coifman, Lions, Meyer和Semmes的Jacobian问题的注记

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Fourier Analysis and Applications Pub Date : 2023-10-20 DOI:10.1007/s00041-023-10041-3

Sauli Lindberg

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引用次数: 5

摘要

Coifman, Lions, Meyer和Semmes在1993年提出了Jacobian算子和其他补偿紧性量是否将它们的自然定义域映射到实变量Hardy空间$$\mathcal {H}^1({\mathbb {R}}^n)$$ h1 (rn)上的问题。在二次算子的情况下，我们给出了一个公理化的巴拿赫空间几何方法。我们在主要的开放情况下也取得了进展，平面上的雅可比方程。

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A Note on the Jacobian Problem of Coifman, Lions, Meyer and Semmes

Abstract Coifman, Lions, Meyer and Semmes asked in 1993 whether the Jacobian operator and other compensated compactness quantities map their natural domain of definition onto the real-variable Hardy space $$\mathcal {H}^1({\mathbb {R}}^n)$$ H 1 ( R n ) . We present an axiomatic, Banach space geometric approach to the problem in the case of quadratic operators. We also make progress on the main open case, the Jacobian equation in the plane.

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来源期刊

Journal of Fourier Analysis and Applications 数学-应用数学

CiteScore

2.10

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics. TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers. Areas of applications include the following: antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications