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A new approach to non-homogeneous local Tb theorems

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Abstract

We develop a new general method to prove various non-doubling local Tb theorems. The method combines the non-homogeneous good lambda method of Tolsa, the big pieces Tb theorem of Nazarov-Treil-Volberg and a new change of measure argument based on stopping time techniques. We also improve known results and discuss some further applications.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, P.O.B. 68, FI-00014, Helsinki, Finland

    Henri Martikainen & Emil Vuorinen

  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona and Centre de Reserca Matemàtica Edifici C Facultat de Ciències, 08193, Bellaterra (Barcelona), Spain

    Mihalis Mourgoglou

  3. Departamento de Matemàticas, Universidad del País Vasco, Aptdo. 644, 48080, Bilbao, Spain

    Mihalis Mourgoglou

  4. Ikerbasque Basque Foundation for Science, Bilbao, Spain

    Mihalis Mourgoglou

Authors
  1. Henri Martikainen
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  2. Mihalis Mourgoglou
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  3. Emil Vuorinen
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Corresponding author

Correspondence to Henri Martikainen.

Additional information

H. M. was supported by the Academy of Finland through the grant Multiparameter dyadic harmonic analysis and probabilistic methods.

H. M. and E. V. are members of the Finnish Centre of Excellence in Analysis and Dynamics Research.

Research of M. M. was supported by the ERC grant 320501 of the European Research Council (FP7/2007-2013). M. M. was also supported by IKERBASQUE and partially supported by the grant MTM-2017-82160-C2-2-P of the Ministerio de Economía y Competitividad (Spain).

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Martikainen, H., Mourgoglou, M. & Vuorinen, E. A new approach to non-homogeneous local Tb theorems. JAMA 143, 95–121 (2021). https://doi.org/10.1007/s11854-021-0147-6

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  • DOI: https://doi.org/10.1007/s11854-021-0147-6

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