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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- Xian-Jin Li
- Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
- Email: firstname.lastname@example.org
- 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