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Weighted norm inequalities for $ k$-plane transforms


Author: B. Rubin
Journal: Proc. Amer. Math. Soc. 142 (2014), 3455-3467
MSC (2010): Primary 44A12; Secondary 47G10
DOI: https://doi.org/10.1090/S0002-9939-2014-11987-3
Published electronically: June 2, 2014
MathSciNet review: 3238421
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Abstract: We obtain sharp inequalities for the $ k$-plane transform, the ``$ j$-plane to $ k$-plane'' transform, and the corresponding dual transforms, acting on $ L^p$ spaces with a radial power weight. The operator norms are explicitly evaluated. Some generalizations and open problems are discussed.


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Additional Information

B. Rubin
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: borisr@math.lsu.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11987-3
Keywords: Radon transforms, weighted norm estimates
Received by editor(s): July 7, 2012
Received by editor(s) in revised form: October 8, 2012
Published electronically: June 2, 2014
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.