A note on the weighted Hilbert's inequality

Author:
Xian-Jin Li

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

Published electronically:
October 14, 2004

MathSciNet review:
2117219

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Abstract | References | Similar Articles | Additional Information

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

DOI:
https://doi.org/10.1090/S0002-9939-04-07606-3

Keywords:
Hilbert transforms,
reproducing kernel Hilbert spaces

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

Article copyright:
© Copyright 2004
American Mathematical Society