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On inversion and Sobolev estimate results about the weighted Radon transform
Author(s) -
Li Wei,
Wang Jinping
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5426
Subject(s) - radon transform , mathematics , sobolev space , radon , fourier transform , inversion (geology) , riesz transform , fractional fourier transform , integral transform , euclidean space , mathematical analysis , sobolev inequality , fourier analysis , geology , physics , quantum mechanics , paleontology , structural basin
In this paper, we derive an inversion of the weighted Radon transform by Fourier transform, Riesz potential, and integral transform. We extend results of Rigaud and Lakhal to the n ‐dimensional Euclidean space. Furthermore, we obtain some properties of the weighted Radon transform. Finally, we develop some estimate results of the weighted Radon transform under Sobolev space.