A Calderon Zygmund decomposition for multiple frequencies and an application to an extension of a lemma of Bourgain

Details A Calderon Zygmund decomposition for multiple frequencies and an application to an extension of a lemma of Bourgain A Calderon Zygmund decomposition for multiple frequencies and an application to an extension of a lemma of Bourgain

2009-12-15

arxiv.org/abs/0912.3010v1

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

We introduce a Calderon Zygmund decomposition such that the bad function has
vanishing integral against a number of pure frequencies. Then we prove a
variation norm variant of a maximal inequality for several frequencies due to
Bourgain. To obtain the full range of Lp estimates we apply the multi frequency
Calderon Zygmund decomposition.

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