scholarly journals Convex curves, Radon transforms and convolution operators defined by singular measures

2000 ◽  
Vol 129 (6) ◽  
pp. 1739-1744 ◽  
Author(s):  
Fulvio Ricci ◽  
Giancarlo Travaglini
Keyword(s):  
Radon Transforms ◽  
Convolution Operators ◽  
Singular Measures ◽  
Convex Curves

scholarly journals Uniform Estimates for Damped Radon Transform on the Plane

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Youngwoo Choi
Keyword(s):  
Radon Transform ◽  
Lorentz Spaces ◽  
Radon Transforms ◽  
Convolution Operators ◽  
Uniform Estimates ◽  
Sharp Estimates ◽  
Rotational Curvature ◽  
Affine Arclength

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.

scholarly journals Convolution operators defined by singular measures on the motion group

2010 ◽  
Vol 59 (6) ◽  
pp. 1935-1946 ◽  
Author(s):  
Luca Brandolini ◽  
Giacomo Gigante ◽  
Sundaram Thangavelu ◽  
Giancarlo Travaglini
Keyword(s):  
Convolution Operators ◽  
Motion Group ◽  
Singular Measures

scholarly journals Singular Measures and Convolution Operators

2006 ◽  
Vol 23 (3) ◽  
pp. 487-490 ◽  
Author(s):  
J. M. Aldaz ◽  
Juan L. Varona
Keyword(s):  
Convolution Operators ◽  
Singular Measures

scholarly journals Endpoint bounds for convolution operators with singular measures

1998 ◽  
Vol 76 (1) ◽  
pp. 35-47 ◽  
Author(s):  
E. Ferreyra ◽  
T. Godoy ◽  
M. Urciuolo
Keyword(s):  
Convolution Operators ◽  
Singular Measures

scholarly journals Radon Transforms in Hyperbolic Spaces and Their Discrete Counterparts

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Enrico Casadio Tarabusi ◽  
Massimo A. Picardello
Keyword(s):  
Radon Transform ◽  
Hyperbolic Spaces ◽  
Spherical Functions ◽  
Homogeneous Tree ◽  
Radon Transforms ◽  
Convolution Operators ◽  
Convolution Kernels

AbstractIn the hyperbolic disc (or more generally in real hyperbolic spaces) we consider the horospherical Radon transform R and the geodesic Radon transform X. Composition with their respective dual operators yields two convolution operators on the disc (with respect to the hyperbolic measure). We describe their convolution kernels in comparison with those of the corresponding operators on a homogeneous tree T, separately studied as acting on functions on the vertices or on the edges. This leads to a new theory of spherical functions and Radon inversion on the edges of a tree.

Boundedness properties of some convolution operators with singular measures

1997 ◽  
Vol 225 (4) ◽  
pp. 611-624 ◽  
Author(s):  
E. Ferreyra ◽  
T. Godoy ◽  
M. Urciuolo
Keyword(s):  
Convolution Operators ◽  
Singular Measures

scholarly journals A CLASS OF STRONGLY SINGULAR RADON TRANSFORMS ON THE HEISENBERG GROUP

2007 ◽  
Vol 50 (2) ◽  
pp. 429-457 ◽  
Author(s):  
Neil Lyall
Keyword(s):  
Fourier Transform ◽  
Heisenberg Group ◽  
Singular Integrals ◽  
Radon Transforms ◽  
Laguerre Functions ◽  
Convolution Operators ◽  
Fourier Transform Methods ◽  
Group Fourier Transform ◽  
Asymptotic Forms ◽  
Singular Radon Transforms

AbstractWe primarily consider here the $L^2$ mapping properties of a class of strongly singular Radon transforms on the Heisenberg group $\mathbb{H}^n$; these are convolution operators on $\mathbb{H}^n$ with kernels of the form $M(z,t)=K(z)\delta_0(t)$, where $K$ is a strongly singular kernel on $\mathbb{C}^n$. Our results are obtained by using the group Fourier transform and uniform asymptotic forms for Laguerre functions due to Erdélyi.We also discuss the behaviour of related twisted strongly singular operators on $L^2(\mathbb{C}^n)$ and obtain results in this context independently of group Fourier transform methods. Key to this argument is a generalization of the results for classical strongly singular integrals on $L^2(\mathbb{R}^d)$.

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