On the Guy David and Jean-Lin Journé T(1) theorem

• Grant number: 19/02997-9
• Support Opportunities: Scholarships in Brazil - Master
• Start date: June 01, 2019
• End date: April 30, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Gustavo Hoepfner
• Grantee: Pedro Henrique Takemura Feitosa da Silva
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 18/14316-3 - Geometric theory of PDE and multidimensional complex analysis, AP.TEM

Abstract

The goal of this research project is to study topics of Harmonic Analysis, Partial Differential Equations and Functional Analysis. The main topic to be addressed is Guy David and Jean-Lin Journée's Theorem T(1) which provide necessary and sufficient conditions for which Calderón-Zygmund operators are bounded in L^2. Generalizations include similar characterizations for boundedness of operators in Hardy, Besov and Triebel-Lizorkin spaces. These characterizations constitute a current research topic and provide solid baggage to anyone involved in this project. (AU)