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Calderón–Zygmund lemma
In mathematics, the Calderón–Zygmund lemma is a fundamental result in Fourier analysis, harmonic analysis, and singular integrals. It is named for the mathematicians Alberto Calderón and Antoni Zygmund.
Given an integrable function , where denotes Euclidean space and denotes the complex numbers, the lemma gives a precise way of partitioning into two sets: one where is essentially small; the other a countable collection of cubes where is essentially large, but where some control of the function is retained.
This leads to the associated Calderón–Zygmund decomposition of , wherein is written as the sum of "good" and "bad" functions, using the above sets.
==Covering lemma==
Let be integrable and be a positive constant. Then there exists an open set such that:
:(1) is a disjoint union of open cubes, , such that for each ,
::
:(2) almost everywhere in the complement of .
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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