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Real Analysis Prelim Camp

Here is where I will upload notes, problems, and solutions for the real analysis prelim camp in Summer, 2020. All the problems come from past UT prelim exams.  Measure Theory – Problems Measure Theory – Solutions Integration and Limits – Problems Integration and Limits – Solutions For problem 11, there is actually an alternative way … Continue reading Real Analysis Prelim Camp

Partial Fourier Sums and Some Probability

These are the lecture notes for a harmonic analysis reading group talk I gave October 14th, 2019 at UT Austin. They are based off of the book Classical and Multilinear Harmonic Analysis Vol. 1 by Muscalu and Schlag Throughout the following notes, we will be working on . Our Fourier transform will be defined to … Continue reading Partial Fourier Sums and Some Probability

Calderon-Zygmund Decomposition Via Martingales

This topic first came up while attending a talk by Daniel Restrepo at the UT Austin harmonic analysis learning seminar last Friday. Daniel gave a basic overview of singular integral operators, and in the process proved and used the classical Calderon-Zygmund decomposition: Theorem 1 (Calderón-Zygmund Decomposition) Given and there exists a collection of almost disjoint … Continue reading Calderon-Zygmund Decomposition Via Martingales