Nonisotropic dilations and the method of rotations with weight
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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.References
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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
- 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
- © Copyright 2011 American Mathematical Society
- 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
- MathSciNet review: 2910766