Weighted inequalities for integral transforms of Fourier type (F-transforms)

• Grant number: 21/13082-1
• Support Opportunities: Scholarships in Brazil - Master
• Effective date (Start): March 01, 2022
• Effective date (End): February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Thaís Jordão
• Grantee: Bruna Zampieri Centurion
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project is based on the study of weighted inequalities for certain types of integral transforms, those with oscillating kernel, known by the name of integral transforms of Fourier type or F-transforms. Classical inequalities such as Pitt's and Hardy-Littlewood's, involving the F-transform given by the Fourier transform, become a consequence of very particular cases of certain weighted inequalities for F-transforms. This proposal aims to understand the weighted inequatilities for F-transforms, in particular for the Fourier transform, the Hankel and Jacobi transforms, and applications to the study of their own decay.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CENTURION, Bruna Zampieri. Weighted norm inequalities for integral transforms of Fourier-type. 2024. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.