Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 
 

 

Square functions with general measures


Authors: Henri Martikainen and Mihalis Mourgoglou
Journal: Proc. Amer. Math. Soc. 142 (2014), 3923-3931
MSC (2010): Primary 42B20
DOI: https://doi.org/10.1090/S0002-9939-2014-12145-9
Published electronically: July 22, 2014
MathSciNet review: 3251732
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] Michael Christ and Jean-Lin Journé, Polynomial growth estimates for multilinear singular integral operators, Acta Math. 159 (1987), no. 1-2, 51-80. MR 906525 (89a:42024), https://doi.org/10.1007/BF02392554
  • [2] A. Grau de la Herran and M. Mourgoglou, A local $ Tb$ theorem for square functions in domains with Ahlfors-David regular boundaries, J. Geom. Anal., to appear, DOI 10.1007/S12220-013-9388-7
  • [3] Steve Hofmann, A local $ Tb$ theorem for square functions, Perspectives in partial differential equations, harmonic analysis and applications, Proc. Sympos. Pure Math., vol. 79, Amer. Math. Soc., Providence, RI, 2008, pp. 175-185. MR 2500492 (2010b:42025)
  • [4] Tuomas P. Hytönen, The sharp weighted bound for general Calderón-Zygmund operators, Ann. of Math. (2) 175 (2012), no. 3, 1473-1506. MR 2912709, https://doi.org/10.4007/annals.2012.175.3.9
  • [5] Tuomas Hytönen and Henri Martikainen, Non-homogeneous $ Tb$ theorem and random dyadic cubes on metric measure spaces, J. Geom. Anal. 22 (2012), no. 4, 1071-1107. MR 2965363, https://doi.org/10.1007/s12220-011-9230-z
  • [6] Tuomas Hytönen, Dachun Yang, and Dongyong Yang, The Hardy space $ H^1$ on non-homogeneous metric spaces, Math. Proc. Cambridge Philos. Soc. 153 (2012), no. 1, 9-31. MR 2943664, https://doi.org/10.1017/S0305004111000776
  • [7] F. Nazarov, S. Treil, and A. Volberg, The $ Tb$-theorem on non-homogeneous spaces, Acta Math. 190 (2003), no. 2, 151-239. MR 1998349 (2005d:30053), https://doi.org/10.1007/BF02392690
  • [8] Stephen Semmes, Square function estimates and the $ T(b)$ theorem, Proc. Amer. Math. Soc. 110 (1990), no. 3, 721-726. MR 1028049 (91h:42018), https://doi.org/10.2307/2047913

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 42B20

Retrieve articles in all journals with MSC (2010): 42B20


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.

American Mathematical Society