Abstract
Let μ be an α-dimensional probability measure. We prove new upper and lower bounds on the decay rate of hyperbolic averages of the Fourier transform μ. More precisely, if H is a truncated hyperbolic paraboloid in Rd we study the optimal β for which / H |μ(Rξ)|2 dσ(ξ) ≤ C(α, μ)R−β for all R > 1. Our estimates for β depend on the minimum between the number of positive and negative principal curvatures of H; if this number is as large as possible our estimates are sharp in all dimensions.
Original language | English (US) |
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Pages (from-to) | 1041-1075 |
Number of pages | 35 |
Journal | Transactions of the American Mathematical Society |
Volume | 374 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2021 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics