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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.

News published in Agência FAPESP Newsletter about the scholarship:
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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.

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