Mathematical Research Letters
Volume 17 (2010)
A Calderón Zygmund decomposition for multiple frequencies and an application to an extension of a Lemma of Bourgain
Pages: 529 – 545
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.