Decay rates of Fourier transforms of curves
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- by B. P. Marshall
- Trans. Amer. Math. Soc. 310 (1988), 115-126
- DOI: https://doi.org/10.1090/S0002-9947-1988-0948194-2
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Abstract:
Let $d\mu$ be a smooth measure on a nondegenerate curve in ${{\mathbf {R}}^n}$. This paper examines the decay rate of spherical averages of its Fourier transform $\widehat {d\mu }$. Thus estimates of the following form are considered: \[ {\left ( {\int _{{\sum _r}} {|\widehat {d\mu }(\xi {|^p}d\xi } } \right )^{1/p}} \leqslant C{r^{ - \sigma }}||f||\] where ${\sum _r} = \{ \xi \in {{\mathbf {R}}^n}:|\xi | = r\}$.References
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Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 310 (1988), 115-126
- MSC: Primary 42B10
- DOI: https://doi.org/10.1090/S0002-9947-1988-0948194-2
- MathSciNet review: 948194