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Examples of measures with slow decay of the spherical means of the Fourier transform

Author: Felipe Ponce Vanegas
Journal: Proc. Amer. Math. Soc. 146 (2018), 2617-2621
MSC (2010): Primary 42B99, 28A80
Published electronically: February 8, 2018
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Abstract: Many authors have studied the rate of average decay of the Fourier transform of measures because of its relationship with the Falconer's conjecture. Although examples have been given showing that the spherical average of the Fourier transform cannot decay always too fast, they usually do not exhibit a single measure decaying sufficiently slow on the whole space. We recover known results using instead single measures.

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Additional Information

Felipe Ponce Vanegas
Affiliation: Department of Mathematics, National University of Colombia, Bogotá 111321, Colombia

Received by editor(s): January 18, 2017
Received by editor(s) in revised form: April 18, 2017, and September 11, 2017
Published electronically: February 8, 2018
Additional Notes: The author was supported by a grant Colciencias N. 6172. The author would also like to thank the Institute of Mathematical Sciences - ICMAT where part of this work was done, for its hospitality. The author wishes to thank Javier Ramos for his support.
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2018 American Mathematical Society

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