Calderon-Zygmund lemma - Wikipedia
harmonic-analysisfourier-analysissingular-integralsmathematics
Abstraction: Decomposition lemma partitioning functions into good and bad parts
Key points:
- Named for Alberto Calderon and Antoni Zygmund; fundamental to Fourier and harmonic analysis
- Given integrable f and threshold alpha, partitions R^d into a "good" region (|f| <= alpha a.e.) and a countable union of open cubes where f is large
- Bad function b = f - g has zero average over each cube; good function g is bounded by 2^d * alpha on the cubes
- Foundational tool for proving boundedness of singular integral operators
- Published by Calderon and Zygmund in Acta Mathematica 1952
Connections: Harmonic Analysis ยท Functional Analysis
Source: http://en.wikipedia.org/wiki/Calder%C3%B3n%E2%80%93Zygmund_lemma