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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on the weighted Hilbert’s inequality
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by Xian-Jin Li PDF
Proc. Amer. Math. Soc. 133 (2005), 1165-1173 Request permission

Abstract:

A finite Hilbert transformation associated with a polynomial is the analogue of a Hilbert transformation associated with an entire function which is a generalization of the classical Hilbert transformation. The weighted Hilbert inequality, which has applications in analytic number theory, is closely related to the finite Hilbert transformation associated with a polynomial. In this note, we study a relation between the finite Hilbert transformation and the weighted Hilbert’s inequality. A question is posed about the finite Hilbert transformation, of which an affirmative answer implies the weighted Hilbert inequality.
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Additional Information
  • Xian-Jin Li
  • Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
  • Email: xianjin@math.byu.edu
  • Received by editor(s): October 21, 2003
  • Received by editor(s) in revised form: December 3, 2003
  • Published electronically: October 14, 2004
  • Additional Notes: This research was supported by National Security Agency MDA 904-03-1-0025
  • Communicated by: Joseph A. Ball
  • © Copyright 2004 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1165-1173
  • MSC (2000): Primary 47B32, 46E22
  • DOI: https://doi.org/10.1090/S0002-9939-04-07606-3
  • MathSciNet review: 2117219