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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper Title:
On the Boundedness of the Discrete Hilbert Transform: An Elementary Proof
Author(s):
R. E. Castillo and H. C. Chaparro
Department of Mathematics,
Universidad Nacional de Colombia,
Bogota,
Colombia..
E-mail: recastillo@unal.edu.co
Program of Mathematics,
Universidad de Cartagena,
Cartagena de Indias,
Colombia.
E-mail:
hchaparrog@unicartagena.edu.co
Abstract:
In this short note, we present an elementary proof of the boundedness of the discrete Hilbert transform on lp(Z)$ spaces for 1 < p < ∞. Our approach relies solely on Hölder's inequality, avoiding more sophisticated tools from harmonic analysis. This offers a simplified and accessible pathway to understanding a classical result in operator theory.
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