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Nonisotropic dilations and the method of rotations with weight


Author: Shuichi Sato
Journal: Proc. Amer. Math. Soc. 140 (2012), 2791-2801
MSC (2010): Primary 42B20, 42B25
DOI: https://doi.org/10.1090/S0002-9939-2011-11188-2
Published electronically: December 19, 2011
MathSciNet review: 2910766
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Abstract: We consider maximal functions $ Mf(x,\theta )$, singular integrals
$ Hf(x,\theta )$, and maximal singular integrals $ H_*f(x,\theta )$ on $ \mathbb{R}^n\times S^{n-1}$ associated with homogeneous curves, for functions $ f$ on $ \mathbb{R}^n$. We prove certain weighted mixed norm estimates for them. These results are applied to the theory of singular integrals with variable kernels via the method of rotations of Calderón-Zygmund.


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Additional Information

Shuichi Sato
Affiliation: Department of Mathematics, Faculty of Education, Kanazawa University, Kanazawa 920-1192, Japan
Email: shuichi@kenroku.kanazawa-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2011-11188-2
Keywords: Singular integrals, homogeneous curves, nonisotropic dilation, method of rotations.
Received by editor(s): November 9, 2010
Received by editor(s) in revised form: March 14, 2011
Published electronically: December 19, 2011
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2011 American Mathematical Society