Tag Archives: Calderon-Zygmund decomposition

Mat-1.C – Harmonic Analysis

For those of you who followed my Harmonic Analysis notes a couple of years back, here is an updated (and slightly more polished) version in pdf  form, from an advanced course I gave at Aalto university: https://noppa.aalto.fi/noppa/kurssi/mat-1.c/harmonic_analysis the notes can … Continue reading

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DMat0101, Notes 6: Introduction to singular integral operators; the Hilbert transform

This week we come to the study of singular integral operators, that is operators of the form defined initially for `nice’ functions . Here we typically want to include the case where has a singularity close to the diagonal which … Continue reading

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DMat0101, Notes 5: The Hardy-Littlewood maximal function

1. Averages and maximal operators This week we will be discussing the Hardy-Littlewood maximal function and some closely related maximal type operators. In order to have something concrete let us first of all define the averages of a locally integrable … Continue reading

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