# name
Muckenhoupt weights and doubling measures

# metadata.dc.description[].value
Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2025.  Director: Martí Prats Soler

# metadata.dc.description.abstract[].value
The main goal of this project is to study Muckenhoupt weights in a context of integration with respect to doubling measures.

The first part is an introduction to measure theory, covering theorems and differentiation of measures. In the second part, we introduce the Calderón–Zygmund decomposition and the Hardy–Littlewood maximal operator, concepts that will be important to study $A_p$ spaces. Finally, the third section is dedicated to the study of the Muckenhoupt weights, characterizing them through inequalities and proving relations between different $A_p$ spaces.

# metadata.dc.rights[].value
cc by-nc-nd (c) Roger Rams Domenech, 2025

# metadata.dc.title[].value
Muckenhoupt weights and doubling measures