Comparison of $T1$ conditions for multi-parameter operators
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- by Ana Grau de la Herrán
- Proc. Amer. Math. Soc. 144 (2016), 2437-2443
- DOI: https://doi.org/10.1090/proc/12891
- Published electronically: October 14, 2015
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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.References
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Bibliographic Information
- Ana Grau de la Herrán
- Affiliation: Department of Mathematics and Statistics, University of Helsinki, Finland
- MR Author ID: 1034208
- Email: ana.grau@helsinki.fi
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2437-2443
- MSC (2010): Primary 42B20
- DOI: https://doi.org/10.1090/proc/12891
- MathSciNet review: 3477059