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Transactions of the American Mathematical Society

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

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On weighted norm inequalities for the Hilbert transform of functions with moments zero
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by Ernst Adams PDF
Trans. Amer. Math. Soc. 272 (1982), 487-500 Request permission

Abstract:

Let $\tilde f$ denote the Hilbert transform of $f$, i.e. \[ \tilde f(x) = {\rm {p}}{\rm {.v}}{\rm {.}}\int {\frac {{f(t)}}{{x - t}}dt} \] and let $1 < p < \infty$. A weight function $w$ is shown to satisfy \[ \int {|\tilde f(x)} {|^p}w(x)dx \le C{\int {|f(x)|} ^p}w(x)dx\] for all $f$ with the first $N$ moments zero, if and only if it is of the form $w(x) = |q(x){|^p}U(x)$, where $q$ is a polynomial of degree at most $N$ and $U \in {A_p}$.
References
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 272 (1982), 487-500
  • MSC: Primary 44A15; Secondary 42A50
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0662048-5
  • MathSciNet review: 662048