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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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 ${\sum _r} = \{ \xi \in {{\mathbf {R}}^n}:|\xi | = r\}$.
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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