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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 582137, 5 pages
http://dx.doi.org/10.1155/2013/582137
Research Article

Uniform Estimates for Damped Radon Transform on the Plane

Department of Mathematics, Ajou University, Suwon 443-749, Republic of Korea

Received 13 May 2013; Accepted 22 August 2013

Academic Editor: Wenchang Sun

Copyright © 2013 Youngwoo Choi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Uniform improving estimates of damped plane Radon transforms in Lebesgue and Lorentz spaces are studied under mild assumptions on the rotational curvature. The results generalize previously known estimates. Also, they extend sharp estimates known for convolution operators with affine arclength measures to the semitranslation-invariant case.