A method for proving Lp-boundedness of singular Radon transforms in codimension 1

2001 ◽  
Vol 108 (2) ◽  
pp. 363-393 ◽  
Author(s):  
Michael Greenblatt
Keyword(s):  
Radon Transforms ◽  
Singular Radon Transforms

scholarly journals Multi-parameter singular Radon transforms II: TheLptheory

2013 ◽  
Vol 248 ◽  
pp. 736-783 ◽  
Author(s):  
Elias M. Stein ◽  
Brian Street
Keyword(s):  
Radon Transforms ◽  
Singular Radon Transforms

A T(1) theorem for singular Radon transforms

2007 ◽  
Vol 339 (3) ◽  
pp. 599-626
Author(s):  
Michael Greenblatt
Keyword(s):  
Radon Transforms ◽  
Singular Radon Transforms

Averages along Polynomial Sequences in Discrete Nilpotent Lie Groups: Singular Radon Transforms

2014 ◽  
Author(s):  
Alexandru D. Ionescu ◽  
Akos Magyar ◽  
Stephen Wainger
Keyword(s):  
Fourier Transform ◽  
Nilpotent Groups ◽  
Nilpotent Lie Groups ◽  
Radon Transforms ◽  
Transform Method ◽  
Polynomial Sequences ◽  
Polynomial Maps ◽  
General Polynomial ◽  
The Fourier Transform ◽  
Singular Radon Transforms

This chapter concentrates on the averages of functions along polynomial sequences in discrete nilpotent groups, illustrating the problems that arise from studying these averages. Though special polynomial sequences can still use the Fourier transform in the central variables to analyze the operators, it appears that one needs to proceed in an entirely different way in the case of general polynomial maps, when the Fourier transform method is not available. This chapter is the first attempt to treat discrete Radon transforms along general polynomial sequences in the non-commutative nilpotent settings. It does so by analyzing the problem of L² boundedness of singular Radon transforms.

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