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On the Upper Majorant Property for Locally Compact Abelian Groups

Published online by Cambridge University Press:  20 November 2018

M. Rains
M. Rains*
Affiliation:
University of A Iberta, Edmonton, Alberta
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Let G be a compact abelian group and form the spaces LP(G) with respect to the normalized Haar measure on G.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 5 , 01 October 1978 , pp. 915 - 925
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Bachelis, G. F., On the upper and lower majorant properties inLp(G), Quart. J. Math., Oxford 2) 24 (1973), 119–128.Google Scholar
2. Boas, R. P., Majorant problems for Fourier series, J. Analyse Math. 10 (1962-3), 253–271.Google Scholar
3. Fournier, J., Majorants andLp-norms, Israel J. Math. 18 (1974), 157–166.Google Scholar
4. Gaudry, G., Topics in harmonic analysis, Lecture Notes, Yale University, 1969.Google Scholar
5. Hardy, G. and Littlewood, J., Notes on the theory of series (XIX): a problem concerning majorants of Fourier series, Quart. J. Math. Oxford (1) 6 (1935), 304–315.Google Scholar
6. Hewit, E. and Ross, K., Abstract harmonic analysis, volume I (Springer-Verlag, New York, 1963).Google Scholar
7. Hewit, E. and Ross, K., Abstract harmonic analysis, volume II (Springer-Verlag, New York, 1970).Google Scholar
8. Lee, E. and Sunouchi, G., On the majorant properties in lp, Bull. Inst. Math. Academia Sinica 4 (1976), 327–336.Google Scholar
9. Lee, E. and Sunouchi, G., On the majorant properties in LP(G), preprint, December 1977.Google Scholar
10. de Leeuw, K., On Lp multipliers, Ann. of Math. (2) 81 (1965), 364–379.Google Scholar
11. Rains, M., Majorant problems in harmonic analysis, Ph.D. Thesis, University of British Columbia, 1976.Google Scholar
12. Reiter, H., Classical harmonic analysis and locally compact groups, Oxford Mathematical Monographs (Oxford University Press, Oxford, 1968).Google Scholar
13. Rudin, W., Positive definite sequences and absolutely monotonie functions, Duke Math. J. 26 (1959), 617–622.Google Scholar
14. Rudin, W., Fourier analysis on groups (Wiley Interscience, New York, 1962).Google Scholar
15. Shapiro, H., Majorant problems for Fourier coefficients, Quart. J. Math. Oxford (2) 26 (1975), 9–18, 16. Zygmund, A., Trigonometric series, Volume I (Cambridge University Press, Cambridge, 1959).Google Scholar