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Comparison of $ T1$ conditions for multi-parameter operators

Author: Ana Grau de la Herrán
Journal: Proc. Amer. Math. Soc. 144 (2016), 2437-2443
MSC (2010): Primary 42B20
Published electronically: October 14, 2015
MathSciNet review: 3477059
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Abstract: When Journé established the classical multi-parameter singular integral theory in 1985, it was formulated in the language of vector-valued Calderón-Zygmund theory. In 2011, Pott and Villarroya formulated a new $ T1$ Theorem for product spaces. In their work, they replaced the vector-valued formulations for several mixed type conditions. Inspired by their work, Martikainen redefined the bi-parameter operators. Originally, it was thought that this new class of operators was larger (and contained the ones defined by Journé). In this paper we prove that both classes are actually equal.

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Additional Information

Ana Grau de la Herrán
Affiliation: Department of Mathematics and Statistics, University of Helsinki, Finland

Received by editor(s): March 10, 2015
Received by editor(s) in revised form: June 10, 2015, and June 29, 2015
Published electronically: October 14, 2015
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society

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