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

• Autores: Fedor Nazarov, Richard Oberlin, Christoph Thiele
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 2-3, 2010, págs. 529-546
• Idioma: inglés
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• Resumen

  • We introduce a Calder\'on 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 Calder\'on Zygmund decomposition.