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TFM_Rams_Domenech_Roger.pdf (590.52 KB)

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Master thesis

Publication date

2025-06-12

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cc by-nc-nd (c) Roger Rams Domenech, 2025
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/228221

Muckenhoupt weights and doubling measures

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Abstract

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.

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Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2025. Director: Martí Prats Soler

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Teoria de la mesura geomètrica, Anàlisi de Fourier, Anàlisi harmònica, Treballs de fi de màster, Roger Rams Domenech

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Geometric measure theory, Fourier analysis, Harmonic analysis, Master's thesis

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Màster Oficial - Matemàtica Avançada

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RAMS DOMENECH, Roger. Muckenhoupt weights and doubling measures. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/228221

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