Geometric Harmonic Analysis
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This thesis is the compilation of the results obtained during my PhD, which started in January 2018 and is being completed in the end of 2021. The main matter is divided into ve chapters, Chapters 2 6. Each of these chapters has its own introductory part, some longer some shorter. This chapter is intended to be an introduction to the whole thesis. Without going into technical details, in this Chapter we will not only motivate the results and the content of the dissertation, but we also explain how and why these results came to be studied. We also introduce the main notation and some preliminary concepts that will be used throughout the dissertation.