The Brascamp–Lieb inequality and its influence on Fourier analysis
Ruixiang Zhang
University of California, Berkeley, United States of America
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Abstract
Brascamp–Lieb inequalities have been important in analysis, mathematical physics and neighboring areas. Recently, these inequalities have had a deep influence on Fourier analysis and, in particular, on Fourier restriction theory. In this chapter we motivate and explain this connection. A lot of our examples are taken from a rapidly developing subarea called “decoupling”. It is the author’s hope that this chapter will be accessible to graduate students in fields broadly related to analysis.