Fourier decay of fractal measures on hyperboloids
Authors:
Alex Barron, M. Burak Erdoğan and Terence L. J. Harris
Journal:
Trans. Amer. Math. Soc. 374 (2021), 1041-1075
MSC (2020):
Primary 42B37
DOI:
https://doi.org/10.1090/tran/8283
Published electronically:
December 3, 2020
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let be an
-dimensional probability measure. We prove new upper and lower bounds on the decay rate of hyperbolic averages of the Fourier transform
. More precisely, if
is a truncated hyperbolic paraboloid in
we study the optimal
for which
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for all



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Additional Information
Alex Barron
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email:
aabarron@illinois.edu
M. Burak Erdoğan
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email:
berdogan@illinois.edu
Terence L. J. Harris
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email:
terence2@illinois.edu
DOI:
https://doi.org/10.1090/tran/8283
Received by editor(s):
April 14, 2020
Received by editor(s) in revised form:
April 29, 2020
Published electronically:
December 3, 2020
Additional Notes:
The second author was partially supported by the Simons collaboration grant, 634269.
Article copyright:
© Copyright 2020
American Mathematical Society