Decay of F-transforms and generalized Besov spaces

• Grant number: 22/11032-0
• Support Opportunities: Regular Research Grants
• Duration: November 01, 2022 - October 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Thaís Jordão
• Grantee: Thaís Jordão
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main interest of this project is to study the relation of generalized Besov spaces and the decay of integral Fourier transformations (F-transformations). In particular, it aims to obtain Titchmarsh-type theorems for integral transformations with oscillating kernels. In this sense, generalized Besov spaces have been used recently to quantify the decay of the Fourier transform, either punctually or through means, and to express it naturally in terms of the original function. In the sense of a reciprocal, a characterization was obtained for the generalized Besov spaces in terms of the decay of the Fourier transform. Results of this nature are called Titchmarsh-type theorems, when the F-transformation involved is the Fourier Transform. (AU)