Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ L^{p}-L^{p'}$ estimates for overdetermined Radon transforms


Authors: Luca Brandolini, Allan Greenleaf and Giancarlo Travaglini
Journal: Trans. Amer. Math. Soc. 359 (2007), 2559-2575
MSC (2000): Primary 42B10, 44A12
Published electronically: January 19, 2007
MathSciNet review: 2286045
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove several variations on the results of F. Ricci and G. Travaglini (2001), concerning $ L^{p}-L^{p'}$ bounds for convolution with all rotations of arc length measure on a fixed convex curve in $ \mathbb{R} ^{2}$. Estimates are obtained for averages over higher-dimensional convex (nonsmooth) hypersurfaces, smooth $ k$-dimensional surfaces, and nontranslation-invariant families of surfaces. We compare Ricci and Travaglini's approach, based on average decay of the Fourier transform, with an approach based on $ L^{2}$ boundedness of Fourier integral operators, and show that essentially the same geometric condition arises in proofs using the two techniques.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 42B10, 44A12

Retrieve articles in all journals with MSC (2000): 42B10, 44A12


Additional Information

Luca Brandolini
Affiliation: Dipartimento di Ingegneria Gestionale e dell’Informazione, Università degli Studi di Bergamo, V.le G Marconi 5, 24044 Dalmine, Italy
Email: brandolini@unibg.it

Allan Greenleaf
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
Email: allan@math.rochester.edu

Giancarlo Travaglini
Affiliation: Dipartimento di Statistica, Università di Milano-Bicocca, Edificio U7, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy
Email: giancarlo.travaglini@unimib.it

DOI: http://dx.doi.org/10.1090/S0002-9947-07-03953-0
PII: S 0002-9947(07)03953-0
Keywords: Radon transform, averages over curves, $L^{p}$ improving
Received by editor(s): December 16, 2003
Received by editor(s) in revised form: February 7, 2005
Published electronically: January 19, 2007
Additional Notes: The second author was partially supported by a grant from the National Science Foundation.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.