1. Calderon-Zygmund decomposition The Calderon-Zygmund decomposition is a key step in the real variable analysis of singular integrals. The idea behind this decomposition is that it is often useful to split an arbitrary integrable function into its “small” and “large” parts, and then use different technique to analyze each part. The scheme is roughly as follows. Given a unction $latex { f}&fg=000000$ and an altitude $latex { \alpha}&fg=000000$, we write $latex { f…
