Decoupling theory has become a cornerstone of modern harmonic analysis. This thesis centers on the detailed proof of the decoupling theorem for the paraboloid, following the groundbreaking work of Bourgain and Demeter. Additionally, we provide a proof of a stronger inequality, the square function estimate for the truncated cone, as established by Guth, Wang, and Zhang; finally, we will discuss various applications of decoupling theory, highlighting the versatility and the importance of this result.
Decoupling theory has become a cornerstone of modern harmonic analysis. This thesis centers on the detailed proof of the decoupling theorem for the paraboloid, following the groundbreaking work of Bourgain and Demeter. Additionally, we provide a proof of a stronger inequality, the square function estimate for the truncated cone, as established by Guth, Wang, and Zhang; finally, we will discuss various applications of decoupling theory, highlighting the versatility and the importance of this result.
Decoupling Estimates for the Paraboloid and the Truncated Cone
MASSERINI, SIMONE
2022/2023
Abstract
Decoupling theory has become a cornerstone of modern harmonic analysis. This thesis centers on the detailed proof of the decoupling theorem for the paraboloid, following the groundbreaking work of Bourgain and Demeter. Additionally, we provide a proof of a stronger inequality, the square function estimate for the truncated cone, as established by Guth, Wang, and Zhang; finally, we will discuss various applications of decoupling theory, highlighting the versatility and the importance of this result.File | Dimensione | Formato | |
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https://hdl.handle.net/20.500.12608/76689