On an apparently bilinear inequality for the Fourier transform
Michael Christ
TL;DR
This paper simplifies a complex bilinear Fourier transform inequality to a linear form, extends the range of exponents, and discusses related mixed-norm inequalities, advancing understanding of Fourier analysis.
Contribution
The paper demonstrates the equivalence of a bilinear inequality to a simpler linear inequality and extends the applicable exponent range.
Findings
Bilinear inequality is equivalent to a linear inequality.
Extended the range of exponents for the inequality.
Discussed related mixed-norm inequalities.
Abstract
A bilinear inequality of Geba, Greenleaf, Iosevich, Palsson, and Sawyer for the Fourier transform is shown to be equivalent to a simpler linear inequality, and the range of exponents is extended. Related mixed-norm inequalities are discussed.
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Taxonomy
TopicsFatigue and fracture mechanics · Mathematical Inequalities and Applications · Numerical methods in inverse problems