Abstract
We generalize Bourgain’s theorem on the decay of the Fourier transform of the multiplicative convolution of measures on ℝ to the ring ℝn, where the multiplication is given by coordinate multiplication.
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Acknowledgement
This is part of the author’s Ph.D. thesis, written under the supervision of Jean-François Quint at the University of Bordeaux. The author wishes to express his thanks to Weikun He and Nicolas de Saxcé for explaining to him their work. The author would like to thank Jean-François Quint for his detailed comments on an earlier version of the paper.
The author would also like to thank the referee for pointing out a mistake and for carefully reading the manuscript.
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Li, J. Discretized Sum-product and Fourier decay in ℝn. JAMA 143, 763–800 (2021). https://doi.org/10.1007/s11854-021-0169-0
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DOI: https://doi.org/10.1007/s11854-021-0169-0