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Master thesis . 2026
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Muckenhoupt weights and doubling measures

descriptionPublicationkeyboard_double_arrow_right Master thesis 17 Mar 2026 Spain English
Authors: Rams Domenech, Roger;

handle: 2445/228221

Muckenhoupt weights and doubling measures

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.

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

Country
Spain
Related Organizations
Keywords

Harmonic analysis, Anàlisi de Fourier, Geometric measure theory, Roger Rams Domenech, Anàlisi harmònica, Master's thesis, Teoria de la mesura geomètrica, Treballs de fi de màster, Fourier analysis

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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