An introduction to the Marcinkiewicz and Lorentz spaces

• Grant number: 18/24862-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2019
• End date: December 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Juliana Conceição Precioso Pereira
• Grantee: Pedro Henrique Rocha Melo
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

The objective of this project is to introduce the student to the study of some variants of the Lebesgue spaces and also to some common techniques used in the area of analysis. Since Lebesgue spaces measure the integrality of a function, they can be seen as the parent of all integrable functions, where finer properties of the functions are sought. One of the attractive features of these variants of the Lebesgue spaces, represented here by Marcinkiewicz spaces (L^ p- weak) and the Lorentz spaces, is that they have good structure and important applications, which makes the subject particularly interesting.