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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

Here are the notes I used to prepare for my Junior Analysis seminar at UT – Austin. Heisenberg’s inequality and the Malgrange-Ehrenpreis Theorem    

Here are the notes for my short presentation on the higher dimensional analog of integration by parts. Packet Packet Solutions Here is the handout for my second presentation and my teaching philosophy. Packet II Teaching Philosophy

Here are my solutions to the exercises assigned for the course Topics in Complex Analysis (Math246C) during the Spring 2018 quarter at UCLA. The original course notes and exercises can be found at Dr. Tao’s Blog.   Math246C, Spring 2018 – Homework 1 Math246C, Spring 2018 – Homework 2 Math246C, Spring 2018 – Homework 3 … Continue reading Topics in Complex Analysis (Solutions)