Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp0137720g37s
 Title: Perturbed Brascamp-Lieb inequalities and application to Parsell-Vinogradov systems Authors: Zhang, Ruixiang Advisors: Sarnak, Peter C Contributors: Mathematics Department Keywords: Brascamp-Lieb inequalityDecouplingParsell-Vinogradov systemPolynomial Method Subjects: Mathematics Issue Date: 2017 Publisher: Princeton, NJ : Princeton University Abstract: In this thesis, we study the perturbed Brascamp-Lieb inequalities and its applications in translation-dilation systems. We prove the endpoint perturbed Brascamp-Lieb inequalities using polynomial partition techniques. We also look at the Parsell-Vinogradov system and verify the Brascamp-Lieb condition holds in its decoupling approach. As a corollary of this and the work of Guo, the main conjecture about the system is true in dimension $2$ and can be proved by the decoupling approach. URI: http://arks.princeton.edu/ark:/88435/dsp0137720g37s Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics