Uniform Estimates for Damped Radon Transform on the Plane

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.

[1]  Youngwoo Choi.  Convolution estimates related to space curves , 2011 .

[2]  D. Oberlin.  Convolution with measures on flat curves in low dimensions , 2009, 0911.1471.

[3]  Betsy Stovall.  Endpoint bounds for a generalized Radon transform , 2009, 0905.3926.

[4]  D. Oberlin,et al.  RESTRICTION OF FOURIER TRANSFORMS TO CURVES II: SOME CLASSES WITH VANISHING TORSION , 2007, Journal of the Australian Mathematical Society.

[5]  C. Yang.  $L^p$ improving estimates for some classes of Radon transforms , 2005 .

[6]  D. Oberlin.  Two estimates for curves in the plane , 2004 .

[7]  Sanghyuk Lee.  Endpoint $L^p-L^q$ estimates for degenerate Radon transforms in ${\mathbb R}^2$ associated with real-analytic functions , 2003 .

[8]  D. Oberlin,et al.  Two endpoint bounds for generalized Radon transforms in the plane , 2002 .

[9]  Sanghyuk Lee.  Remarks on the degenerate Radon transform in , 2001 .

[10]  D. Oberlin.  Convolution with measures on hypersurfaces , 2000, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  Jong-Guk Bak.  An Lp-Lq estimate for Radon transforms associated to polynomials , 2000 .

[12]  D. Oberlin.  Convolution with affine arclength measures in the plane , 1999 .

[13]  Elias M. Stein,et al.  Models of degenerate Fourier integral operators and Radon transforms , 1994 .

[14]  A. Seeger.  Degenerate Fourier integral operators in the plane , 1993 .

[15]  K. Guo,et al.  Convolution estimates related to surfaces of half the ambient dimension , 1991, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  S. Drury.  Degenerate curves and harmonic analysis , 1990, Mathematical Proceedings of the Cambridge Philosophical Society.

[17]  Sanghyuk Lee.  Endpoint $L^p$-$L^q$ estimates for some classes of degenerate Radon transforms in $\Real^2$ , 2004 .

[18]  S. Lee.  REMARKS ON THE DEGENERATE RADON TRANSFORM IN R , 2001 .

[19]  A. Seeger.  Radon transforms and finite type conditions , 1998 .

[20]  M. Christ.  On the restriction of the Fourier transform to curves: endpoint results and the degenerate case , 1985 .