Multi-parameter singular integral operators and representation theorem

• Yumeng Ou ^[1]
  1. [1] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 1, 2017, págs. 325-350
• Idioma: inglés
• DOI: 10.4171/RMI/939
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• Resumen

  • We formulate a class of singular integral operators in arbitrarily many parameters using mixed type characterizing conditions. The main result we prove for this class of operators is a multi-parameter representation theorem stating that a generic operator in our class can be represented as an average of sums of dyadic shifts, which implies a new multi-parameter T1 theorem as a byproduct. This extends the representation principles of Hytönen’s and Martikainen’s to the multi-parameter setting. Furthermore, equivalence between ours and Journé’s class of multi-parameter operators is established, whose proof requires the multiparameter T1 theorem.