Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

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.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B32, 46E22

Retrieve articles in all journals with MSC (2000): 47B32, 46E22


Additional Information

Xian-Jin Li
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: xianjin@math.byu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07606-3
PII: S 0002-9939(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