Mathematical Research Letters

Volume 17 (2010)

Number 3

A Calderón Zygmund decomposition for multiple frequencies and an application to an extension of a Lemma of Bourgain

Pages: 529 – 545



Fedor Nazarov (University of Wisconsin, Madison)

Richard Oberlin (University of Califoria, Los Angeles)

Christoph Thiele (University of Califoria, Los Angeles)


We introduce a Calderón 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 $L^p$ estimates we apply the multi frequency Calderón Zygmund decomposition.

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