A note on the weighted Hilbert's inequality
Author:
XianJin Li
Journal:
Proc. Amer. Math. Soc. 133 (2005), 11651173
MSC (2000):
Primary 47B32, 46E22
Published electronically:
October 14, 2004
MathSciNet review:
2117219
Fulltext PDF Free Access
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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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Additional Information
XianJin Li
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email:
xianjin@math.byu.edu
DOI:
http://dx.doi.org/10.1090/S0002993904076063
PII:
S 00029939(04)076063
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 9040310025
Communicated by:
Joseph A. Ball
Article copyright:
© Copyright 2004
American Mathematical Society
