A note on the weighted Hilbert’s inequality

Li, Xian-Jin

doi:10.1090/S0002-9939-04-07606-3

A note on the weighted Hilbert’s inequality
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by Xian-Jin Li

Proc. Amer. Math. Soc. 133 (2005), 1165-1173

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

Published electronically: October 14, 2004

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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.

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