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Square functions with general measures


Authors: Henri Martikainen and Mihalis Mourgoglou
Journal: Proc. Amer. Math. Soc. 142 (2014), 3923-3931
MSC (2010): Primary 42B20
Published electronically: July 22, 2014
MathSciNet review: 3251732
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Abstract: We characterize the boundedness of square functions in the upper half-space with general measures. The short proof is based on an averaging identity over good Whitney regions.


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Additional Information

Henri Martikainen
Affiliation: Département de Mathématiques, Bâtiment 425, Faculté des Sciences d’Orsay, Université Paris-Sud 11, F-91405 Orsay Cedex, France
Address at time of publication: Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, 00014 Helsinki, Finland
Email: henri.martikainen@helsinki.fi

Mihalis Mourgoglou
Affiliation: Département de Mathématiques, Bâtiment 425, Faculté des Sciences d’Orsay, Université Paris-Sud 11, F-91405 Orsay Cedex, France
Email: mourgoglou@ihes.fr

DOI: https://doi.org/10.1090/S0002-9939-2014-12145-9
Keywords: Square function, non-homogeneous analysis
Received by editor(s): December 15, 2012
Published electronically: July 22, 2014
Additional Notes: The first author was supported by the Emil Aaltonen Foundation
The second author was supported by Fondation de Mathématiques Jacques Hadamard (FMJH)
The authors wish to thank Université Paris-Sud 11, Orsay, for its hospitality
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.