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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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$L^p$ boundedness of discrete singular Radon transforms
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by Alexandru D. Ionescu and Stephen Wainger PDF
J. Amer. Math. Soc. 19 (2006), 357-383 Request permission

Abstract:

We prove that if $K:\mathbb {R}^{d_1}\to \mathbb {C}$ is a Calderón–Zygmund kernel and $P:\mathbb {R}^{d_1}\to \mathbb {R}^{d_2}$ is a polynomial of degree $A\geq 1$ with real coefficients, then the discrete singular Radon transform operator \begin{equation*} T(f)(x)=\sum _{n\in \mathbb {Z}^{d_1}\setminus \{0\}}f(x-P(n))K(n) \end{equation*} extends to a bounded operator on $L^p(\mathbb {R}^{d_2})$, $1<p<\infty$. This gives a positive answer to an earlier conjecture of E. M. Stein and S. Wainger.
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Additional Information
  • Alexandru D. Ionescu
  • Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Van Vleck Hall, Madison, Wisconsin 53706
  • MR Author ID: 660963
  • Email: ionescu@math.wisc.edu
  • Stephen Wainger
  • Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Van Vleck Hall, Madison, Wisconsin 53706-1313
  • MR Author ID: 179960
  • Email: wainger@math.wisc.edu
  • Received by editor(s): February 27, 2004
  • Published electronically: October 24, 2005
  • Additional Notes: The first author was supported in part by an NSF grant and an Alfred P. Sloan research fellowship
    The second author was supported in part by an NSF grant
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 19 (2006), 357-383
  • MSC (1991): Primary 11L07, 42B20
  • DOI: https://doi.org/10.1090/S0894-0347-05-00508-4
  • MathSciNet review: 2188130