Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 3778162
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 42B99, 28A80

Retrieve articles in all journals with MSC (2010): 42B99, 28A80

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