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Inequalities with Weights for Discrete Hilbert Transforms✝

Published online by Cambridge University Press:  20 November 2018

Kenneth F. Andersen
Kenneth F. Andersen*
Affiliation:
Dept. of Math. University of Alberta Edmonton, Alberta
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Let Z(Z+) denote the set of all (positive) integers and let T denote the discrete Hilbert transform defined for suitable sequences a = {ak}kϵz by

where as usual the prime denotes omission of the term k = n.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 9 - 16
Copyright
Copyright © Canadian Mathematical Society 1977

Footnotes

✝

Research supported in part by NRC Grant #A-8185.

References

1. Andersen, K. F., Discrete Hilbert Transforms and Rearrangement Invariant Sequence Spaces, Applicable Analysis 5 (1976), pp. 193-200.Google Scholar
2. Andersen, K. F., Weighted Norm Inequalities for Hilbert Transforms and Conjugate Functions of Even and Odd Functions, Proc. Amer. Math. Soc. 56 (1976), pp. 99-107.Google Scholar
3. Hardy, G. H., Littlewood, J. E., and Polya, G., "Inequalities", 2nd Ed., Cambridge University Press, 1952.Google Scholar
4. Hunt, R., Muckenhoupt, B., and Wheeden, R., Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform, Trans. Amer. Math. Soc. 176 (1973), pp. 227-251.Google Scholar
5. Muckenhoupt, B., Weighted Norm Inequalities for the Hardy Maximal Function, Trans. Amer. Math. Soc. 165 (1972), pp. 207-226.Google Scholar