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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
Published electronically: October 14, 2004
MathSciNet review: 2117219
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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.

References [Enhancements On Off] (What's this?)

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Additional Information

Xian-Jin Li
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602

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

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